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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #151 : How To Solve Two Step Equations

Solve for .

10x+98=18

Possible Answers:

11.6

-11.6

Correct answer:

Explanation:

In order to solve for , we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

10x+98=18

Subtract from both sides of the equation.

10x+98-98=18-98

Remember since is greater than and is negative, our answer is negative. We will treat treat this operation as a subtraction problem.

10x=-(98-18)

Simplify.

10x=-80

Divide both sides of the equation by .

$\frac{10x}{10}=\frac{-80}{10}$

Solve. When dividing a negative number by a positive number, our answer becomes negative.

x=-8

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Example Question #152 : How To Solve Two Step Equations

Solve for .

$\frac{x}{6}+8=5$

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

$\frac{x}{6}+8=5$

Subtract from both sides of the equation.

$\frac{x}{6}+8-8=5-8$

Remember since is greater than and is negative, our answer is negative. We will treat this operation as a subtraction problem.

$\frac{x}{6}=-\left ( 8-5\right )$

Simplify.

$\frac{x}{6}=-3$

Multiply both sides of the equation by .

$(6)\frac{x}{6}=-3(6)$

Solve. When multiplying a negative number by a positive number, our answer is negative.

x=-18

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Example Question #161 : How To Solve Two Step Equations

Solve for .

$\frac{x}{5}+9=-10$

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

$\frac{x}{5}+9=-10$

Subtract from both sides of the equation.

$\frac{x}{5}+9-9=-10-9$

When subtracting a negative number from another negative number, we will treat it as an addition problem and then add a negative sign to the sum.

$\frac{x}{5}=-(10+9)$

Simplify.

$\frac{x}{5}=-19$

Multiply both sides of the equation by .

$(5)\frac{x}{5}=-19(5)$

Solve. When multiplying a negative number by a positive number, our answer is negative.

x=-95

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Example Question #162 : How To Solve Two Step Equations

Solve for .

6x-9=111

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

6x-9=111

Add to both sides of the equation.
6x-9+9=111+9

Simplify.

6x=120

Divide both sides of the equation by .

$\frac{6x}{6}=\frac{120}{6}$

Solve.

x=20

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Example Question #161 : How To Solve Two Step Equations

Solve for .

7x-19=-47

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

7x-19=-47

Add to both sides of the equation.

7x-19+19=-47+19

Remember since is greater than and is negative, our answer is negative. We will treat this operation as a subtraction problem.

7x=-(47-19)

Simplify.

7x=-28

Divide both sides of the equation by .

$\frac{7x}{7}=\frac{-28}{7}$

Solve. When dividing a negative number with a positive number, our answer becomes negative.

x=-4

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Example Question #164 : How To Solve Two Step Equations

Solve for .

-4x-19=21

Possible Answers:

x=-10

Correct answer:

x=-10

Explanation:

In order to solve for , we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

-4x-19=21

Add to both sides of the equation.
-4x-19+19=21+19

Simplify.

-4x=40

Divide both sides of the equation by .

$\frac{-4x}{-4}=\frac{40}{-4}$

Solve. When dividing a positive number with a negative number, our answer becomes negative.

x=-10

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Example Question #162 : How To Solve Two Step Equations

Solve for .

$\frac{x}{4}-6=3$

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

$\frac{x}{4}-6=3$

Add to both sides of the equation.

$\frac{x}{4}-6+6=3+6$

Simplify.

$\frac{x}{4}=9$

Multiply both sides of the eqaution by .

$(4)\frac{x}{4}=9(4)$

Solve.

x=36

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Example Question #163 : How To Solve Two Step Equations

Solve for .

$\frac{x}{11}-9=-18$

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

$\frac{x}{11}-9=-18$

Add to both sides of the equation.

$\frac{x}{11}-9+9=-18+9$

Remember since is greater than and is negative, our answer is negative. We will treat this operation as a subtraction problem.

$\frac{x}{11}=-(18-9)$

Simplify.

$\frac{x}{11}=-9$

Multiply both sides of the equation by .

$(11)\frac{x}{11}=-9(11)$

Solve. When multiplying a negative number by a positive number, our answer is negative.

x=-99

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Example Question #164 : How To Solve Two Step Equations

Solve for .

$\frac{x}{-3}-8=-17$

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

$\frac{x}{-3}-8=-17$

Add to both sides of the equation.

$\frac{x}{-3}-8+8=-17+8$

Remember since is greater than and is negative, our answer is negative. We will treat this operation as a subtraction problem.

$\frac{x}{-3}=-(17-8)$

Simplify.

$\frac{x}{-3}=-9$

Multiply both sides of the equation by .

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

Solve. When multiplying a negative number by a negative number, our answer is positive.

x=27

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Example Question #165 : How To Solve Two Step Equations

Solve the equation below.

6p + 4p + 3 = 7 (p - 2)

Possible Answers:

$p = 5\frac{2}{3}$

$p = -\frac{17}{3}$

$p = -\frac{5}{17}$

$p = \frac{2}{3}$

$p = -\frac{17}{5}$

Correct answer:

$p = -\frac{17}{3}$

Explanation:

6p + 4p + 3 = 7 (p - 2)

Combine like terms on the left and use distributive property on the right.

Use properties of equality to balance the equation.

10p + 3 = 7p -14

-7p -7p

3p + 3 = -14

3p = -17

$p = -\frac{17}{3}$

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #151 : How To Solve Two Step Equations

Example Question #152 : How To Solve Two Step Equations

Example Question #161 : How To Solve Two Step Equations

Example Question #162 : How To Solve Two Step Equations

Example Question #161 : How To Solve Two Step Equations

Example Question #164 : How To Solve Two Step Equations

Example Question #162 : How To Solve Two Step Equations

Example Question #163 : How To Solve Two Step Equations

Example Question #164 : How To Solve Two Step Equations

Example Question #165 : How To Solve Two Step Equations

All Algebra 1 Resources

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