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Algebra 1 : How to solve two-step equations

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Example Questions

Example Question #11 : How To Solve Two Step Equations

Solve for the value of .

3x + 4 = 13

Possible Answers:

x = 9

x = 3

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

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

x = -3

Correct answer:

x = 3

Explanation:

For the equation 3x + 4 = 13 , a set of two operations can be used to determine the value of .

First, subtract from both sides of the equation to isolate the variable with its coefficient.

3x + 4 = 13

(3x +4 ) - 4 = (13) - 4

3x = 9

Second, divide both sides of the equation by the coefficient to isolate the variable and its value.

3x = 9

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

x = 3

The value of is .

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Example Question #12 : How To Solve Two Step Equations

Solve this equation:

8a - 5 + 2(a+1) = -3(a + 6)

Possible Answers:

$a = -\frac{13}{15}$

$a = \frac{10}{13}$

$a = \frac{15}{13}$

$a =- \frac{15}{13}$

$a = \frac{13}{15}$

Correct answer:

$a =- \frac{15}{13}$

Explanation:

8a - 5 + 2(a+1) = -3(a + 6)

Begin by multiplying out all of the terms by the distributive property:

8a - 5 + 2a + 2 = -3a -18

Then, combine like terms on both sides of the equation:

10a -3 = -3a -18

Add to both sides of the equation:

10a + 3a -3 = -3a + 3a -18 , or

13a -3 = -18

Add 3 to both sides:

13a -3 +3 = -18 + 3 , or

13a = -15

Finally, divide both sides by 13 to give the final answer:

$a =- \frac{15}{13}$

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Example Question #544 : Linear Equations

Solve for in the equation below.

$2(x+3) - 4 = \; 3(x-2) +3$

Possible Answers:

Correct answer:

Explanation:

$2(x+3) - 4 = \; 3(x-2) +3$

Use the distributive property to eliminate the parantheses.

(2x)+(2*3)-4=(3x)-(3*2)+3

2x+6-4=3x-6+3

Combine like terms.

2x + 2 = 3x - 3

Now we need to isolate . We can add to both sides of the equation, then subtract from both sides.

2x+2+3=3x-3+3

2x+5=3x

2x+5-2x=3x-2x

5=x

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Example Question #12 : How To Solve Two Step Equations

Solve for :

3x-1=6x+7-x

Possible Answers:

Correct answer:

Explanation:

3x-1=6x+7-x can be simplified into 3x-1=5x+7 . If you move the 's to one side and the integers to the other, you will end up with -2x=8 . Divide both sides by , and you get x=-4 .

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Example Question #546 : Linear Equations

Solve for :

6x-3-2x=2x+1

Possible Answers:

Correct answer:

Explanation:

6x-3-2x=2x+1

can be simplified to

4x-3=2x+1 .

Next, you move the 's to one side and the integers to the other side (i.e. subtract from both sides and add 3 to both sides).

This gives you

2x=4

which lets you come to

x=2 .

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Example Question #547 : Linear Equations

$Solve\; for\; y \; in \; the\; equation,\frac{3y}{2}-\frac{3}{2}=0$

Possible Answers:

$\frac{2}{3}$

Correct answer:

Explanation:

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Example Question #548 : Linear Equations

Solve for :

2(2x-3)=10x-3(x+1)

Possible Answers:

Correct answer:

Explanation:

First, use the distributive property on 2(2x-3)=10x-3(x+1) to get 4x-6=10x-3x-3 . Next, combine the 's on the right side of the equation to get 4x-6=7x-3 . Then, add 3 and subtract from both sides to separate the 's and integers: -3=3x . Finally, divide both sides by 3 to get the solution of x=-1 .

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Example Question #549 : Linear Equations

Solve for :

4 (x +4) + 9 = 5 (x + 5) - x

Possible Answers:

There is no solution.

can be any real number.

x=1

x = 25

x=0

Correct answer:

can be any real number.

Explanation:

4 (x +4) + 9 = 5 (x + 5) - x

$4 \cdot x +4 \cdot 4 + 9 = 5 \cdot x + 5 \cdot 5 - x$

4 x +16 + 9 = 5x + 25 - x

4 x + 25 = 4x + 25

This identically true statement is an indication that the solution set is the set of all real numbers.

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Example Question #551 : Linear Equations

Solve for :

4 (x +7) + 2 = 5 (x + 4) - x

Possible Answers:

There is no solution.

x = 1

x = 0

can be any real number.

x = 10

Correct answer:

There is no solution.

Explanation:

4 (x +7) + 2 = 5 (x + 4) - x

$4 \cdot x +4 \cdot 7 + 2 = 5 \cdot x + 5 \cdot 4 - x$

4 x +28+ 2 = 5x + 20- x

4 x +30 = 4x + 20

30 = 20

This identically false statement is an indication that there is no solution.

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Example Question #552 : Linear Equations

Solve for :

4 (x +9) + 9 = 5 (x + 9) - x

Possible Answers:

x=0

x=45

There is no solution.

can be any real number.

x=1

Correct answer:

can be any real number.

Explanation:

4 (x +9) + 9 = 5 (x + 9) - x

$4 \cdot x +4 \cdot 9 + 9 = 5 \cdot x + 5 \cdot 9 - x$

4 x +36 + 9 = 5x + 45 - x

4 x + 45 = 4x + 45

This identically true statement is an indication that the solution set is the set of all real numbers.

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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 #11 : How To Solve Two Step Equations

Example Question #12 : How To Solve Two Step Equations

Example Question #544 : Linear Equations

Example Question #12 : How To Solve Two Step Equations

Example Question #546 : Linear Equations

Example Question #547 : Linear Equations

Example Question #548 : Linear Equations

Example Question #549 : Linear Equations

Example Question #551 : Linear Equations

Example Question #552 : Linear Equations

All Algebra 1 Resources

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