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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #831 : Linear Equations

Solve for :

4x- 4 = 20

Possible Answers:

-6

Correct answer:

Explanation:

To get by itself, first add 4 to both sides of the equation:

4x - 4 = 20

4x = 24

Then, divide each side of the equation by 4:

4x=24

x = 6

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Example Question #292 : How To Solve Two Step Equations

Solve for .

$5x^{2}=80$

Possible Answers:

$\frac{\sqrt{80}}{\sqrt{5}}$

$\sqrt{1.26}$

Correct answer:

Explanation:

Divide each side of the equation by 5.

$x^{2}=16$

Take the square root of each side of the equation.

x=4

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Example Question #832 : Linear Equations

Solve for .

$\frac{4p}{5}+8 = 4$

Possible Answers:

None of the other answers

Correct answer:

Explanation:

Subtract 8 from each side of the equation.

$\frac{4p}{5}=-4$

Multiply each side of the equation by $\frac{5}{4}$ (the inverse of $\frac{4}{5}$ ).

$p=\frac{-4}{1}\times\frac{5}{4}=\frac{-20}{4}=-5$

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Example Question #833 : Linear Equations

Solve for .

7(x+3)=70

Possible Answers:

$\frac{7}{6}$

Correct answer:

Explanation:

7(x+3)=70

Distribute 7 to the term in parentheses

7x+21=70

Subtract 21 from each side of the equation

7x=49

Divide each side by 7

x=7

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Example Question #1 : How To Solve Absolute Value Equations

Solve the absolute value equation:

$\left | \frac{x-4}{3} \right| = \left | x +2 \right|$

Possible Answers:

$\small \varnothing$ (no solution)

$\small \left \{-5, -1 \right\}$

$\left \{-5 \right \}$

$\left \{-5, -\frac{1}{2} \right \}$

Correct answer:

$\left \{-5, -\frac{1}{2} \right \}$

Explanation:

An equation that equates two absolute value functions allows us to choose one of the absolute value functions and treat it as the constant. We then separate the equation into the "positive" version, $\tiny \small \frac{x-4}{3}=x+2$ , and the "negative" version, $\tiny \small \frac{x-4}{3} = -(x+2)$ . Solving each equation, we obtain the solutions, and $\tiny \tiny -\frac{1}{2}$ , respectively.

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Example Question #1 : How To Solve Absolute Value Equations

Solve for x.

|x+3|=4

Possible Answers:

No solution

x = –3, 4

x = –7, 1

x = 4, 7

x = 1, 7

Correct answer:

x = –7, 1

Explanation:

First, split into two possible scenarios according to the absolute value.

x+3=4

x+3=-4

Looking at , we can solve for x by subtracting 3 from both sides, so that we get x = 1.

Looking at x+3=-4 , we can solve for x by subtracting 3 from both sides, so that we get x = –7.

So therefore, the solution is x = –7, 1.

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Example Question #2 : How To Solve Absolute Value Equations

Find the solution to x for |x – 3| = 2.

Possible Answers:

2, 5

1, 4

1, 5

2, 4

Correct answer:

1, 5

Explanation:

|x – 3| = 2 means that it can be separated into x – 3 = 2 and x – 3 = –2.

So both x = 5 and x = 1 work.

x – 3 = 2 Add 3 to both sides to get x = 5

x – 3 = –2 Add 3 to both sides to get x = 1

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Example Question #2 : How To Solve Absolute Value Equations

Solve for x:

$\small \left | x+2 \right |=12$

Possible Answers:

$\small x=-14$ or $\small x=10$

$\small x=-10$

$\small x=14$ or $\small x=-10$

$\small x=10$

Correct answer:

$\small x=-14$ or $\small x=10$

Explanation:

Because of the absolute value signs,

$\small x+2=12$ or $\small x+2=-12$

Subtract 2 from both sides of both equations:

$\small x+2-2=12-2$ or $\small x+2-2=-12-2$

$\small x=10$ or $\small x=-14$

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Example Question #2 : How To Solve Absolute Value Equations

Solve for :

$|x-4|=\frac{5}{8}$

Possible Answers:

$x=4\frac{5}{8}, -4\frac{3}{8}$

$x=4\frac{5}{8}, -3\frac{5}{8}$

$x=4\frac{5}{8}, -3\frac{3}{8}$

$x=4\frac{3}{8}, -3\frac{3}{8}$

$x=4\frac{5}{8}$

Correct answer:

$x=4\frac{5}{8}, -3\frac{3}{8}$

Explanation:

$|x-4|=\frac{5}{8}$

There are two answers to this problem:

$x-4=\frac{5}{8}$

$x=\frac{5}{8}+4=4\frac{5}{8}$

and

$-(x-4)=\frac{5}{8}$

$4-x=\frac{5}{8}$

$-x=\frac{5}{8}-4=-3\frac{3}{8}$

$x=-3\frac{3}{8}$

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Example Question #6 : How To Solve Absolute Value Equations

If x = 2 , evaluate $\left | -4x + 3\right | \left | 3x-14\right |$ .

Possible Answers:

220

Correct answer:

Explanation:

An absolute value expression differs from a normal expression only in its sign. Instead of being a positive or negative quantity, an absolute value represents a scalar distance from zero, so it does not have a sign. For example, $\left | -2\right |$ is the same as $\left | 2\right |$ because both represent a value 2 units away from zero. In this problem, $\left | -4x + 3\right |$ equals $\left | -5 \right |$ , or 5. $\left | 3x - 14\right |$ equals 8. The final answer is (5)(8) or 40.

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #831 : Linear Equations

Example Question #292 : How To Solve Two Step Equations

Example Question #832 : Linear Equations

Example Question #833 : Linear Equations

Example Question #1 : How To Solve Absolute Value Equations

Example Question #1 : How To Solve Absolute Value Equations

Example Question #2 : How To Solve Absolute Value Equations

Example Question #2 : How To Solve Absolute Value Equations

Example Question #2 : How To Solve Absolute Value Equations

Example Question #6 : How To Solve Absolute Value Equations

All Algebra 1 Resources

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