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Algebra 1 : How to solve two-step equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #751 : Algebra 1

Solve: -10x+5=-5

Possible Answers:

$\frac{1}{10}$

$-\frac{1}{10}$

Correct answer:

Explanation:

To isolate the unknown variable, first subtract five from both sides.

-10x+5-5=-5-5

Simplify both sides.

-10x=-10

Divide by negative ten on both sides to isolate .

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

Simplify both sides. A negative divided by a negative will result in a positive number.

x=1

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Example Question #221 : How To Solve Two Step Equations

Solve for x: 2 x + 1 = 15

Possible Answers:

Correct answer:

Explanation:

To solve, go against the order of opperation, PEMDAS. This means addition and subtraction go first. This means that we should first subtract 1 from both sides:

2x = 14

divide both sides by 2

x = 7

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Example Question #753 : Algebra 1

Solve for w: $\frac{w-1}{4} = 1$

Possible Answers:

$\frac{3}{4}$

$-\frac{3}{4}$

1.25

Correct answer:

Explanation:

To solve, go against the order of opperations, PEMDAS. Consider the whole top of the fraction as being in parentheses.

This means that first we will multiply both sides by 4:

$\frac{w - 1 }{4} *4 = 1*4$

w - 1 = 4 now add 1 to both sides

w = 5

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Example Question #222 : How To Solve Two Step Equations

Solve for :

$\frac{25}{x} = 5$

Possible Answers:

$\frac{1}{5}$

2.5

$5\frac{1}{5}$

Correct answer:

Explanation:

This is a two-step equation that simply requires moving the variable around before isolating it. To start, move to the other side of the equation (and out of the denominator) by multiplying both sides by :

$\frac{25}{x} = 5$ Multiply left and right by

25 = 5x Divide both sides by

x = 5

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Example Question #223 : How To Solve Two Step Equations

Solve for :

15y + 45 = 510

Possible Answers:

Correct answer:

Explanation:

First isolate the variable containing term by subtracting from both sides of the equation:

15y + 45 = 510

15y = 465

Next divide both sides by to solve for

$465 \div 15 = 31$

y = 31

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Example Question #224 : How To Solve Two Step Equations

Solve: 6-x=16

Possible Answers:

Correct answer:

Explanation:

In order to solve for x, we need to do two steps.

Add on both sides to move the variable to the right side of the equation.

6-x+x=16+x

Simplify the left side.

6=16+x

Subtract sixteen from both sides.

6-16=16+x-16

Simplify both sides.

-10=x

The answer is:

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Example Question #225 : How To Solve Two Step Equations

Solve: 3x-9 = 62

Possible Answers:

$\frac{53}{3}$

$\frac{71}{3}$

Correct answer:

$\frac{71}{3}$

Explanation:

To solve for , first add nine on both sides.

3x-9+9 = 62+9

Simplify both sides.

3x=71

Divide by three on boths sides.

$\frac{3x}{3}=\frac{71}{3}$

Simplify both sides. The right side cannot be simplified any further.

$x=\frac{71}{3}$

The answer is: $\frac{71}{3}$

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Example Question #226 : How To Solve Two Step Equations

Solve: $\frac{5}{6}x-\frac{6}{5}=\frac{5}{6}$

Possible Answers:

$x=-\frac{25}{61}$

None of these answers

$x=\frac{61}{25}$

$x=\frac{25}{61}$

$x=-\frac{61}{25}$

Correct answer:

$x=\frac{61}{25}$

Explanation:

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

Add $\frac{6}{5}$ to both sides:

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

Find a common denominator and combine the right side:

$\frac{5}{6}x=\frac{25}{30}+\frac{36}{30}$

$\frac{5}{6}x=\frac{61}{30}$

Multiply both sides by $\frac{6}{5}$ :

$\frac{6}{5}*\frac{5}{6}x=\frac{61}{30}*\frac{6}{5}$

$\mathbf{x=\frac{61}{25}}$

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Example Question #761 : Linear Equations

Solve the equation: 6x-4=10

Possible Answers:

$\frac{7}{3}$

$\frac{14}{6}$

$-\frac{14}{6}$

$-\frac{7}{3}$

$\frac{12}{5}$

Correct answer:

$\frac{7}{3}$

Explanation:

Add four on both sides to bring the four to the right side of the equation.

6x-4+4=10+4

Simplify both sides.

6x=14

Divide both sides by six.

$x=\frac{14}{6}$

This fraction is not reduced. Reduce the fraction by writing out the factors.

$x=\frac{14}{6} =\frac{2\times 7}{2 \times 3}$

Cancel out or divide the twos.

The answer is: $\frac{7}{3}$

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Example Question #762 : Linear Equations

Solve: 5x+3 = -18

Possible Answers:

$-\frac{33}{5}$

$-\frac{21}{5}$

$\frac{21}{5}$

Correct answer:

$-\frac{21}{5}$

Explanation:

Subtract three from both sides.

5x+3-3 = -18-3

Simplify.

5x=-21

Divide by five on both sides.

$\frac{5x}{5}=\frac{-21}{5}$

Simplify both sides of the equation.

$x=-\frac{21}{5}$

The answer is: $-\frac{21}{5}$

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Algebra 1 : How to solve two-step equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #751 : Algebra 1

Example Question #221 : How To Solve Two Step Equations

Example Question #753 : Algebra 1

Example Question #222 : How To Solve Two Step Equations

Example Question #223 : How To Solve Two Step Equations

Example Question #224 : How To Solve Two Step Equations

Example Question #225 : How To Solve Two Step Equations

Example Question #226 : How To Solve Two Step Equations

Example Question #761 : Linear Equations

Example Question #762 : Linear Equations

All Algebra 1 Resources

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