# Algebra 1 Help | Free Algebra 1 Lessons & Practice Problems

Go through the lessons and practice problems below to help you learn Algebra 1 and excel in school. We’ll track your progress and help you identify your strengths and weaknesses. Algebra 1 help is available to everyone, but you need to create an account in order to access the practice questions and track your progress.

### Lesson: Verbal to Algebraic Expressions & Equations

Example: How do you write 5 greater than $x$ algebraically?

### Lesson: Declaring Variables

Example: Mike is 3 inches taller than Semande. If Semande is s inches tall, express Mike’s height in terms of s.

### Lesson: Order of Operations

Example: Evaluate $3 - (5-8)^2$

### Lesson: Order of Operations with Substitution

Example: If $x=2$, what is the value of $2x^2-3x$?

### Lesson: Adding and Subtracting Real Numbers

Example: Evaluate $5 - (-2)$

### Lesson: Multiplying and Dividing Real Numbers

Example: Evaluate $-3 \times 4$

### Lesson: Properties of Real Numbers

Example: Which property justifies the following equation: $5(x+2y)+5=5x+10y+5$

### Lesson: Distributive Property

Example: Simplify $3(4x-5)$

### Lesson: Finding the Solution to an Equation

Example: Is 7 a solution to the equation $12 = 3x - 9$?

### Lesson: Solving Algebraic Equations (One-Step)

Example: Solve for $x$.
$x+7=12$

### Lesson: Solving Multi-Step Equations

Example: Solve for $x$.
$2x + 4 = 18$

### Lesson: Multi-Step Equations (Variable on Both Sides)

Example: Solve for $x$.
$2x - 4 = -3x + 11$

### Lesson: Linear Equations

Example: Solve for $y$.
$3y + 2x = 12$

### Lesson: Solving Proportions

Example: Solve for $x$.
$\dfrac{x}{6} = \dfrac{20}{15}$

### Lesson: Solving Complex Proportions

Example: Solve for $x$.
$\dfrac{x+5}{4} = \dfrac{3}{8}$

### Lesson: Percents

Example: What is 48% of 30?

### Lesson: Percent Change

Example: What is the percent change from 50 to 72?

### Lesson: Graphing Inequalities

Example: Graph k < 1

### Lesson: Solving Inequalities Using Addition or Subtraction

Example: Solve for $x$.
$x - 12 > 8$

### Lesson: Solving Inequalities Using Multiplication or Division

Example: Solve for $x$.
$-4x \geq 12$

### Lesson: Solving Inequalities

Example: Solve for $x$.
$-7x + 19 \leq -2$

### Lesson: Solving Compound Inequalities

Example: Solve for $x$.
$-3 \leq 2x -5$ < $21$

### Lesson: Solving and Graphing Compound Inequalities

Example: Solve for $x$ and graph.
$0 \leq r + 5$ < $9$

### Lesson: Absolute Value Equations

Example: Solve for $p$.
$9 + |5p + 1| = 18$

### Lesson: Absolute Value Inequalities

Example: Solve for $x$.
$3|5x + 1|$ > $12$

### Lesson: Using Graphs to Relate Two Quantities

Example: A bird flies above ground in search of worms. This is represented in the table below.

What does A represent?

### Lesson: Patterns and Linear Functions

Example: Is the following graph linear?

Example: For each set of ordered pairs, write the rule that represents the function.
$(0, 3), (1, 8), (2, 13), (3, 18), (4, 23)$

### Lesson: Patterns and Non-Linear Functions

Example: Is the following a linear or nonlinear function?

Example: For the set of ordered pairs, write the rule that represents the function.
(0,1),(1,3),(2,9),(3,27),(4,81)

### Lesson: Graphing a Function Rule

Example: Match the function with its graph.

### Lesson: Writing a Function Rule

Example: Write the function rule for the table of values.

### Lesson: Formalizing Relations and Functions

Example: Is the following relation shown a function?
(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)

### Lesson: Slope

Example: What is the slope of the line below?

Example: What is the slope of the line that passes through the points (2, 7) and (5, 12)?

### Lesson: Point Slope Form

Example: What is the point-slope form of a line passing through the point (1,2) with a slope of -2?

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### Lesson: Standard Form of the Equations of a Line

Example: What is the standard form equation of the line $30-3y=15x$?

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### Lesson: Equations of Parallel and Perpendicular Lines

Example: What is the equation of the line that passes through (2,4) and is parallel to $y=3x-1$
Example: What is the equation of the line that passes through (2,4) and is perpendicular to $y=3x-1$

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### Lesson: Scatterplots and Trendlines

Example: If the trend continues, what is the expected y-value when x is 8, based on the scatterplot shown below?

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### Lesson: Solving a System of Equations Graphically

Example: Solve the following system of equations graphically: $y=2x+3$ and $y=-3x+3$

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### Lesson: Solving a System of Equations Graphically

Example: Solve the following system of equations graphically: $y=x-7$ and $y=-4x+1$

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### Lesson: Solving a System of Equations Using Substitution

Example: Solve the following system of equations by using substitution: $y=5x+5$ and $y=-2x$

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### Lesson: Solving a System of Equations Using Substitution

Example: Solve the following system of equations by using substitution: $y=x$ and $y=-7x+3$

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### Lesson: Solving a System of Equations Using Elimination

Example: Solve the following system of equations by using elimination: $3x+2y=15$ and $-6x+5y=3$

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### Lesson: Solving a System of Equations Using Elimination

Example: Solve the following system of equations by using elimination: $2x+3y=10$ and $3x-2y=3$

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### Lesson: Applications of Linear Systems

Example: The difference between two numbers is 4. Their sum is 18. What are the two numbers?

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### Lesson: Word Problems – System of Equations

Example: Smith and Jones are selling cookies. Smith sold 4 chocolate chip and 6 sugar cookies for a total of $60. Jones sold 5 chocolate chip and 3 sugar cookies for a total of$30. How much does a chocolate chip cookie cost?

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### Lesson: Word Problems – System of Equations

Example: Rose is selling tickets to the school play to the first and second graders. The first graders bought 12 tickets for Friday night and 15 tickets to Saturday night for a total of $400. The second graders bought 14 tickets to Friday night and 10 tickets to Saturday night for a total of$420. How much does a Friday night ticket cost?

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### Lesson: Graphing Linear Inequalities

Example: Sketch the solution to the system of inequalities: $y \textless 3x-5$ and $y \geq -2x+1$

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### Lesson: Solving a System of Linear Inequalities

Example: What is the solution to the following system of inequalities: $y \geq x+4$ and $y \leq 6x-1$

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### Lesson: Exponential Growth

Example: The population of an ant colony increases by 100 each year. Is this linear or exponential growth?

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### Lesson: Exponential Decay

Example: Is the function $y=4^{-x}+2$ exponential decay?

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### Lesson: Factor Out the Greatest Common Factor

Example: Factor out the GCF from $9x^3 + 3x^2$

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### Lesson: Factoring by Grouping

#### IX. Quadratic Functions and Equations

Example: Evaluate $y=x^2 +3x -2$ at $x=2$

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### Lesson: Properties of Quadratic Functions

Example: Is the point (3,7) a solution to the function $y=x^2 +x -5$?

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### Lesson: Solving Quadratic Equations by Taking Square Roots

Example: What are the solutions to $x^2 = 16$?

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### Lesson: Solving Equations by Factoring

Example: What are the solutions to $x^2 +9x +18$?

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### Lesson: Completing the Square

Example: What should be the value for $c$ when completing the square for $a^2 -8a +c$?

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### Lesson: Solve Equations by Completing the Square

Example: Find the solutions to $x^2 +6x -10=0$ by completing the square

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### Lesson: Vertex Form of a Quadratic Function by Completing the Square

Example: Complete the square to find the vertex of $y=x^2 +8x -12$

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### Lesson: Solving a System of Equations Graphically (Linear & Quadratic)

Example: Solve the following system of equations graphically: $y=x^2+4x+4$ and $y=x+2$

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### Lesson: Solving a System of Equations Using Substitution (Linear & Quadratic)

Example: Solve the following system of equations by using substitution: $y=x^2 -4x +12$ and $y=3x$

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### Lesson: Pythagorean Theorem

Example: If the legs of a right triangle measure 5 and 12, what is the length of the hypotenuse?

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Example: Simplify $\sqrt{3x^3} \cdot \sqrt{2x}$

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Example: Simplify $\dfrac{\sqrt{5x^2 y^3}}{\sqrt{x^3 y^4}}$

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### Lesson: SOHCAHTOA (sine, cosine, tangent)

Example: In $\triangle ABC$, $\angle C$ is a right angle, $m\angle A = 30 \textdegree$, and $\overline{AB} = 10$. What is the measure of $\overline{BC}$?

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### Lesson: Inverse Trigonometric Functions

Example: Given that $\triangle ABC$ is a right triangle with $\angle C$ as the right angle, $\overline{AB} = 12$ and $\overline{BC} = 7$. What is the measure of $\angle A$?

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### Lesson: Multiplying and Dividing Rational Expressions

Example: Simplify $\dfrac{2}{3} \cdot \dfrac{6x^3}{8}$

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### Lesson: Dividing Polynomials

Example: Simplify $\dfrac{10x^4 - 15x}{5x^2}$

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### Lesson: Adding and Subtracting Rational Expressions

Example: Simplify $\dfrac{3-x}{x^2+3x-1} + \dfrac{3-x}{x^2+3x-1}$

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### Lesson: Fractional Equations

Example: Solve for x: $\dfrac{2}{x} + \dfrac{3}{8} = \dfrac{10}{x}$

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### Lesson: Solving Rational Equations

Example: Solve for x: $\dfrac{5}{x^2} - \dfrac{2}{3x} = \dfrac{4}{x}$

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### Lesson: Inverse Variation

Example: If $y$ varies inversely with $x$, and $y=15$ when $x=2$, find $x$ when $y$ is $8$

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### Lesson: Measures of Central Tendency & Dispersion

Example: James scored a 91 and a 94 on his first two tests. What score must he receive on his third test to maintain a 90 average?

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### Lesson: Box & Whisker Plot

Example: What is the interquartile range for the following set of data: 2,5,3,7,5,6,2,2,9,4

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### Lesson: Samples and Surveys

Example: John is trying to find out how many students in his school prefer math class over english class. He surveys every 5th ninth grader who walks into school. Is this sample biased?

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### Lesson: Theoretical vs. Experimental Probability

Example: Joanna rolled a six-sided die. What is the theoretical probability that it will land on an even number?

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### Lesson: Probability of Compound Events

Example: Patricia rolled a six-sided die twice. What is the probability that she rolls a 2 and then an odd number?

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