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Pre-Algebra : Algebraic Equations

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Example Questions

Example Question #32 : Two Step Equations With Integers

Solve the following equation:

3x-1=26

Possible Answers:

Correct answer:

Explanation:

In order to solve this equation, you have to isolate the variable to one side by reversing the operations done to it. Whatever is done on one side of the equals sign must be done on the other side of the equals sign as well. When the variable is by itself, it will be defined as whatever is left on the other side of the equals sign, and the equation is solved.

3x-1=26

Add to both sides of the equation.

3x-1+1=26+1

3x=27

Divide each side by .

$\frac{3x}{3}=\frac{27}{3}$

$x=\frac{27}{3}$

x=9

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Example Question #33 : Two Step Equations With Integers

Solve the following equation:

x^2+2=18

Possible Answers:

Correct answer:

Explanation:

x^2+2=18

Subtract from each side of the equation.

x^2+2-2=18-2

x^2=18-2

x^2=16

Take the square root of each side of the equation and solve for the unknown.

$\sqrt{x^2}=\sqrt{16}$

$x=\sqrt{16}$

$x=\sqrt{4*4}$

x=4

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Example Question #34 : Two Step Equations With Integers

Solve for .

|x-4|=2

Possible Answers:

$x=6\ \textup{or}\ x=2$

$x=-2\ \textup{or}\ x=2$

$x=4\ \textup{or}\ x=2$

x=2

x=6

Correct answer:

$x=6\ \textup{or}\ x=2$

Explanation:

To "break" or remove the absolute value, we can create two different equations.

We can say

x-4=2

and

x-4=-2

When we solve each of these equations, we get x= 6 and x=2.

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Example Question #35 : Two Step Equations With Integers

Solve for :

3x+5=11

Possible Answers:

Correct answer:

Explanation:

Explanation:

The goal is to isolate the variable to one side.

3x+5=11

Subtract from each side of the equation:

3x+5-5=11-5

3x=6

Divide each side by :

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

x=2

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Example Question #31 : Two Step Equations With Integers

Solve for :

-3t+2=8

Possible Answers:

t=2

t=1

t=-1

t=-2

Correct answer:

t=-2

Explanation:

-3t+2=8

-3t+2-2=8-2

-3t=6

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

t=-2

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Example Question #37 : Two Step Equations With Integers

Solve the problem below for .

2x + 4 = 3x - 9

Possible Answers:

x = 1

x = 2

x = 13

x = -5

x = 20

Correct answer:

x = 13

Explanation:

2x + 4 = 3x - 9

You must put your 's and numbers on opposite sides of the equation. First, you subtract from both sides of the equation:

2x + 4 -2x= 3x - 9-2x

Then, you will have by itself on the right side of the equation:

4= x - 9

Next, you add to both sides of the equation to put all of the numbers on the same side of the equation:

4+9= x - 9+9

13= x

Once you do this, you have found that x=13 .

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Example Question #38 : Two Step Equations With Integers

Solve for

10x+5=20x-5

Possible Answers:

x=-1

x=1

x=10

x=3

x=2

Correct answer:

x=1

Explanation:

1.) Add 5 to both sides, removing the "". It now reads 10x+10=20x .

2.) Subtract 10x from both sides, removing the " 10x ". It now reads 10=10x .

3.) Divide both sides by 10, resulting in x=1

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Example Question #39 : Two Step Equations With Integers

Solve for

6(x+5)=17x - 25

Possible Answers:

x=7

x=6

x=11

x=5

x=8

Correct answer:

x=5

Explanation:

1.) Distribute the 6, which ends up as 6x+30=17x-25 .

2.) Add 25 to both sides, removing the "". It now reads 6x+55=17x

3.) Subtract from both sides, removing the "". It now reads 55=11x

4.) Divide both sides by 11, resulting in 5=x

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Example Question #40 : Two Step Equations With Integers

Solve for :

15z+ 70 = 280

Possible Answers:

$23 \frac{1}3{}$

210

Correct answer:

Explanation:

15z + 70 = 280

Subtract from both sides

15z= 210

Divide both sides by

z = 14

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Example Question #41 : Two Step Equations

Solve for :

$q ^{2}+ 116 = 165$

Possible Answers:

116

$\pm$

281

Correct answer:

$\pm$

Explanation:

$q ^{2}+ 116 = 165$

Subtract 116 from both sides

Find the square root of

$= \pm7$

Remember that a negative number squared returns a positive so there are possible solutions

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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #32 : Two Step Equations With Integers

Example Question #33 : Two Step Equations With Integers

Example Question #34 : Two Step Equations With Integers

Example Question #35 : Two Step Equations With Integers

Example Question #31 : Two Step Equations With Integers

Example Question #37 : Two Step Equations With Integers

Example Question #38 : Two Step Equations With Integers

Example Question #39 : Two Step Equations With Integers

Example Question #40 : Two Step Equations With Integers

Example Question #41 : Two Step Equations

All Pre-Algebra Resources

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