To review these concepts, go to Simplifying Expressions and Solving Equation Word Problems Study Guide.

**Simplifying Expressions and Solving Equation Word Problems Practice Questions**

**Practice 1**

**Problems**

Simplify each of the following expressions:

- 4
*x*+ 10*x*= _____ - 20
*y*– 3*y*= _____ - –9
*x*^{2}+ 6*x*^{2}– 2*x*= _____ - 2(
*x*– 4) = _____ - 7(2
*y*+ 5) = _____

**Solutions**

- 14
*x* - 17
*y* - –3
*x*^{2}– 2*x* - 2
*x*– 8 - 14
*y*+ 35

**Practice 2**

**Problems**

Solve each of the following equations.

*x*+ 10 = 25- 3
*x*– 5 = 10 - 12
*x*– 3*x*= 18 - 5(
*x*+ 1) = 30 - 2
*x*+ 10 = 3(*x*– 4)

**Solutions**

*x*+ 10 – 10 = 25 – 10- 3
*x*– 5 + 5 = 10 + 5 - 12
*x*– 3*x*= 18 - 5(
*x*+ 1) = 30 - 2
*x*+ 10 = 3(*x*– 4)

*x* = 15

3*x* = 15

*x* = 5

9*x* = 18

*x* = 2

5*x* + 5 = 30

5*x* + 5 – 5 = 30 – 5

5*x* = 25

*x* = 5

2*x* + 10 = 3*x* – 12

2*x* – 2*x* + 10 = 3*x* – 2*x* – 12

10 = *x* – 12

10 + 12 = *x* – 12 + 12

*x* = 22

**Practice 3**

**Problems**

- Six times a number is equal to 300. What is the number?
- A number decreased by 7 is equal to the product of 4 and 10. What is the number?
- The sum of five and a number is equal to twice the number. What is the number?
- Three times the sum of a number and 1 is equal to 21. What is the number?
- Thirty-one minus a number is the same as twice a number plus 10. What is the number?

**Solutions**

*Read and understand the question*. This question is looking for a number when clues about this number are given.*Read and understand the question*. This question is looking for a number when clues about this number are given.*Read and understand the question*. This question is looking for a number when clues about this number are given.*Read and understand the question*. This question is looking for a number when clues about this number are given.*Read and understand the question*. This question is looking for a number when clues about this number are given.

*Make a plan*. Translate the statement into equation form. Then, solve the equation using the equation solving steps.

*Carry out the plan*. Let *x* = a number. The key phrase *six times a number* is written as 6*x*, so the equation is 6*x* = 300. Divide each side by 6 to get the variable alone.

*x*= 50

*Check your answer*. Check your solution by substituting the answer into the equation.

- 6

*x*= 300

becomes

- 6(50) = 300

- 300 = 300

This answer is checking.

*Make a plan*. Translate the statement into equation form. Then, solve the equation using the equation solving steps.

*Carry out the plan*. Let *x* = a number. The key phrase *decreased* by means subtraction, so the first part of the statement translates to *x* – 7. In the second part of the sentence, the key word *product* means multiplication, so multiply 4 by 10 to get 40. The entire equation is *x* – 7 = 40. Get the variable alone by adding 7 to each side. The equation simplifies to *x* = 47.

*Check your answer*. Check your solution by substituting the answer into the equation.

*x*– 7 = 4 × 10

becomes

- 47 – 7 = 40

- 40 = 40

This answer is checking.

*Make a plan*. Translate the statement into equation form. Then, solve the equation using the equation solving steps.

*Carry out the plan*. Let *x* = a number. The key word *sum* means addition, so the first part of the statement translates to *x* + 5. In the second part of the sentence, *twice the number* is written as 2*x*. The entire equation is *x* + 5 = 2*x*. Get the variables on one side of the equation by subtracting *x* from each side.

*x*–

*x*+ 5 = 2

*x*–

*x*

The equation simplifies to

- 5 =

*x*

*Check your answer*. Check your solution by substituting the answer into the equation.

*x*+ 5 = 2

*x*

becomes

- 5 + 5 = 2(5)

- 10 = 10

This answer is checking.

*Make a plan*. Translate the statement into equation form. Then, solve the equation using the equation solving steps.

*Carry out the plan*. Let *x* = a number. The key word *sum* means addition, so the sum of a number and 1 is written as *x* + 1. Multiply this expression by 3 and set it equal to 21. The statement translates to

- 3(

*x*+ 1) = 21

Apply the distributive property.

- 3

*x*+ 3 = 21

Subtract 3 from each side of the equation to get 3*x* = 18. Next, divide each side by 3 to get the variable alone.

*x*= 6

*Check your answer*. Check your solution by substituting the answer into the equation.

- 3(

*x*+ 1) = 21

becomes

- 3(6 + 1) = 21

- 3(7) = 21

- 21 = 21

This answer is checking.

*Make a plan*. Translate the statement into equation form. Then, solve the equation using the equation solving steps.

*Carry out the plan*. Let *x* = a number. The first part of the statement translates to 31 – *x*. In the second part of the sentence, *twice a number plus 10* is written as 2*x* + 10. The entire equation is

- 31 –

*x*= 2

*x*+ 10

Get the variables on one side of the equation by adding *x* to each side.

- 31 –

*x*+

*x*= 2

*x*+

*x*+ 10

The equation simplifies to 31 = 3*x* + 10

Subtract 10 from each side of the equation to get 21 = 3*x*. Next, divide each side by 3 to get the variable alone.

*x*= 7

*Check your answer*. Check your solution by substituting the answer into the equation.

- 31 –

*x*= 2

*x*+ 10

becomes

- 31 – 7 = 2(7) + 10

- 24 = 14 + 10

- 14 = 14

This answer is checking.

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