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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #47 : How To Solve Absolute Value Equations

Solve for .

$\left | \frac{x}{6} \right |=8$

Possible Answers:

$\pm1.5$

$\pm48$

1.5

Correct answer:

$\pm48$

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation 1:

$\frac{x}{6} =8$

Multiply on both sides. x=48 .

Equation 2:

$\frac{-x}{6}=8$

Multiply on both sides and divide on both sides. x=-48 .

Therefore, the solutions are, $x=\pm48$ .

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Example Question #48 : How To Solve Absolute Value Equations

Solve for .

$\left | \frac{x}{7}+3 \right |=9$

Possible Answers:

42, 84

42, -84

Correct answer:

42, -84

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation1:

$\frac{x}{7}+3 =9$

Subtract on both sides and then multiply on both sides to get x=42 .

Equation2:

$-(\frac{x}{7}+3)=9$

By distributing the negative sign, we have: $-\frac{x}{7}-3=9$ . Add to both sides and multiply both sides by , we get x=-84 .

Therefore, the solutions are,

x=42, -84 .

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Example Question #49 : How To Solve Absolute Value Equations

Solve.

$\left | 2x-3\right |-7=0$

Possible Answers:

No solution

$x=3\ \text{or}\ x=-5$

$x=-5\ \text{or}\ x=5$

$x=-2\ \text{or}\ x=5$

$x=-1\ \text{or}\ x=-5$

Correct answer:

$x=-2\ \text{or}\ x=5$

Explanation:

$\left | 2x-3\right |-7=0$

$\left | 2x-3\right |=7$

$(2x-3)=7\ \text{or} -(2x-3)=7$

$2x=7+3\ \text{or}\ 2x=-7+3$

$2x=10\ \text{or}\ 2x=-4$

$x=5\ \text{or}\ x=-2$

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Example Question #50 : How To Solve Absolute Value Equations

Solve for :

$\left | x+7\right |=7$

Possible Answers:

Correct answer:

Explanation:

We define the absolute value of a number as that number's distance from on the number line. Given $\left | x+7\right |=7$ , we therefore must solve for two possibilities:

1.) x+7=7 , or

2.) x+7=-7

Solving #1, we get:

x+7=7

x=0

Solving #2, we get:

x+7=-7

x=-14

Consequently, the solution is x=0 or x=-14 .

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Example Question #51 : How To Solve Absolute Value Equations

Solve for :

$\left | 2x-6\right |=8$

Possible Answers:

Correct answer:

Explanation:

We define the absolute value of a number as that number's distance from on the number line. Given $\left | 2x-6\right |=8$ , we therefore must solve for two possibilities:

1.) 2x-6=8 , or

2.) 2x-6=-8

Solving #1, we get:

2x-6=8

2x=14

x=7

Solving #2, we get:

2x-6=-8

2x=-2

x=-1

Therefore, the solution is x=7 or x=-1 .

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Example Question #881 : Linear Equations

Solve for :

$\left | \frac{1}{9}x\right |=-10$

Possible Answers:

Does Not Exist

$\frac{9}{10}$

$-\frac{9}{10}$

Correct answer:

Does Not Exist

Explanation:

We define the absolute value of a number as that number's distance from on the number line.

Given

$\left | \frac{1}{9}x\right |=-10$ ,

we know that the absolute value cannot exist because distance can never be described as a negative number.

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Example Question #51 : How To Solve Absolute Value Equations

$\left | 3x\right |+7=28$

Possible Answers:

x=-7,7

x=-11.7,7

x=7

x=-12,12

x=-7,11.7

Correct answer:

x=-7,7

Explanation:

Before we can solve for x, we must isolate the absolute value symbol on one side of the equation. To do that, we must subtract from both sides, leaving us with

$\left | 3x\right |=21$

Next, we must make two equations: 3x=-21 and 3x=21 .

From here, it is a simple one-step equation, in which we divide both sides by . This gives us

x=-7,7 .

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Example Question #51 : How To Solve Absolute Value Equations

Solve for :

$\left | x+2\right |=9$

Possible Answers:

Correct answer:

Explanation:

We define the absolute value of a number as that number's distance from on the number line.

Given $\left | x+2\right |=9$ , we therefore must solve for two possibilities:

1.) x+2=9 , or

2.) x+2=-9

Solving #1, we get:

x+2=9

x=7

Solving #2, we get:

x+2=-9

x=-11

Consequently, the solution is x=7 or x=-11 .

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Example Question #52 : How To Solve Absolute Value Equations

Solve for :

$\left | 4x-5\right |=7$

Possible Answers:

or $\frac{1}{2}$

or $-\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

or $-\frac{1}{2}$

Explanation:

We define the absolute value of a number as that number's distance from on the number line.

Given $\left | 4x-5\right |=7$ , we therefore must solve for two possibilities:

1.) 4x-5=7 , or

2.) 4x-5=-7

Solving #1, we get:

4x-5=7

4x=12

x=3

Solving #2, we get:

4x-5=-7

4x=-2

$x=-\frac{1}{2}$

Consequently, the solution is x=3 or $x=-\frac{1}{2}$ .

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Example Question #52 : How To Solve Absolute Value Equations

Solve for :

$\left | 5x+6\right |-1=7$

Possible Answers:

$\frac{2}{5}$ or $-\frac{14}{5}$

$\frac{14}{5}$

$-\frac{14}{5}$

$-\frac{2}{5}$ or $\frac{14}{5}$

$\frac{2}{5}$

Correct answer:

$\frac{2}{5}$ or $-\frac{14}{5}$

Explanation:

We define the absolute value of a number as that number's distance from on the number line.

Given $\left | 5x+6\right |-1=7$ , or $\left | 5x+6\right |=8$ we therefore must solve for two possibilities:

1.) 5x+6=8 , or

2.) 5x+6=-8

Solving #1, we get:

5x+6=8

5x=2

$x=\frac{2}{5}$

Solving #2, we get:

5x+6=-8

5x=-14

$x=-\frac{14}{5}$

Consequently, the solution is $x=\frac{2}{5}$ or $x=-\frac{14}{5}$ .

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #47 : How To Solve Absolute Value Equations

Example Question #48 : How To Solve Absolute Value Equations

Example Question #49 : How To Solve Absolute Value Equations

Example Question #50 : How To Solve Absolute Value Equations

Example Question #51 : How To Solve Absolute Value Equations

Example Question #881 : Linear Equations

Example Question #51 : How To Solve Absolute Value Equations

Example Question #51 : How To Solve Absolute Value Equations

Example Question #52 : How To Solve Absolute Value Equations

Example Question #52 : How To Solve Absolute Value Equations

All Algebra 1 Resources

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