Simplifying Expressions and Solving Equation Word Problems Practice Questions

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Simplifying Expressions and Solving Equation Word Problems Practice Questions

Practice 1

Problems

Simplify each of the following expressions:

1. 4x + 10x = _____
2. 20y – 3y = _____
3. –9x² + 6x² – 2x = _____
4. 2(x – 4) = _____
5. 7(2y + 5) = _____

Solutions

1. 14x
2. 17y
3. –3x² – 2x
4. 2x – 8
5. 14y + 35

Practice 2

Problems

Solve each of the following equations.

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

Solutions

1. x + 10 – 10 = 25 – 10

x = 15

2. 3x – 5 + 5 = 10 + 5

3x = 15

x = 5

3. 12x – 3x = 18

9x = 18

x = 2

4. 5(x + 1) = 30

5x + 5 = 30

5x + 5 – 5 = 30 – 5

5x = 25

x = 5

5. 2x + 10 = 3(x – 4)

2x + 10 = 3x – 12

2x – 2x + 10 = 3x – 2x – 12

10 = x – 12

10 + 12 = x – 12 + 12

x = 22

Practice 3

Problems

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

Solutions

1. 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 6x, so the equation is 6x = 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.

6x = 300

becomes

6(50) = 300
300 = 300

This answer is checking.

2. 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 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.

3. 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 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 2x. The entire equation is x + 5 = 2x. Get the variables on one side of the equation by subtracting x from each side.

x – x + 5 = 2x – x

The equation simplifies to

5 = x

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

x + 5 = 2x

becomes

5 + 5 = 2(5)
10 = 10

This answer is checking.

4. 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 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.

3x + 3 = 21

Subtract 3 from each side of the equation to get 3x = 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.

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

31 – x = 2x + 10

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

31 – x + x = 2x + x + 10

The equation simplifies to 31 = 3x + 10

Subtract 10 from each side of the equation to get 21 = 3x. 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 = 2x + 10

becomes

31 – 7 = 2(7) + 10
24 = 14 + 10
14 = 14

This answer is checking.