Free Printable #060 Solving & Setting Up Equations

Worksheets

#060 Solving & Setting Up Equations

Total questions: 50

Worksheet time: 40mins

Name

Class

Date

Translate into an algebraic equation.

One-half of x is equal to 3.

\frac{x}{2}\ =\ 3

$\frac{1}{2}\ =\ 3$

$\frac{1}{2}\ =\ 3x$

$\frac{1}{x}=3$

Translate into an algebraic equation.

The difference between y and 23 is 12.

y + 23 = 12

y - 23 = 12

y - 12 = 23

y + 12 = 23

Translate into an algebraic equation.

Eleven times x is thirty-three.

11x = 33

11 + x = 33

11 - x = 33

11/x = 33

Translate into an algebraic equation.

N minus 2 is equal to 16.

N - 2 = 16

N - 16 = 2

2N = 16

N + 2 = 16

Translate into an algebraic equation.

The total of m and 3 is 21.

m - 3 = 21

m + 3 = 21

3m = 21

m/3 = 21

Translate into an algebraic equation.

Two multiplied by b is equal to 8.

2b = 8

8b = 2

28 = b

2 + b = 8

Translate into an algebraic equation.

The sum of x and 3 is 5.

x + 3 = 5

3x = 5

x - 3 = 5

x + 5 = 3

Read and interpret.

Janice had x colored pencils in her box and shares them equally with her friend, Talia. Her brother gives her 2 more colored pencils. Janice now has 3 pencils in her box.

$\frac{x}{2}+3=2$

$2x-2=3$

$\frac{x}{2}-2=3$

$\frac{x}{2}+2=3$

Read/interpret.

Mr. Hewitt estimates the cost towards a fresh coat of paint for the exterior of his home. He makes a provision for 12 gallons of paint priced at $x per gallon. The cost of miscellaneous expenses was $2,264. The total estimated cost for painting the exterior of his home was $2,624.

12x - 2264 = 2624

12x + 2624 = 2264

12x + 2264 = 2624

12x + 2624 = - 2264

10.

Read/interpret.

A meteorologist measured the average rainfall received in Cities A & B. The cities received 11 inches of rainfall in total. While City A received x inches of rain, City B experienced three times the amount of rainfall than City A.

x + 3x = 11

x - 3x = 11

3x - x = 11

11 = - 3x - x

11.

Read/interpret.

Timothy spent a total of $68 at Macys. His purchases included a pair of jeans at $32 and 2 t-shirts at $x each.

2x - 32 = 68

2x + 32 = 68

2x + 32 = -68

2x + 68 = 32

12.

Read/interpret.

A customer at a Mexican diner placed an order for 3 buritto bowls which were priced at $x each. He also ordered a plate of corn tacos at $12.96. He was billed a total of $32.46.

3x + 12.96 = 32.46

2x - 32.46 = 12.96

2x + 12.96 = 32.46

3x - 12.96 = 32.46

13.

What is the first step in solving this equation?

Add 4 to each side

Subtract 4 from each side

Subtract 2y from each side

Divide each side by 2y

14.

The steps in solving 5b - 6 = 24 are:

Add 6 to both sides and then divide both sides by 5

Add 6 to both sides and then multiply both sides by 5

Subtract 6 from both sides and then multiply both sides by 5

Subtract 6 from both sides and then divide both sides by 5

15.

What is a 1-step problem?

A problem where multiple operations are present.

A problem where the variable is missing.

An equation where only one step is needed to solve it.

An equation where two steps are needed to solve it.

16.

What is a 2-step problem?

An equation where 2 steps are needed to solve it.

An equation where only one step is needed to solve it.

A problem with only one operation present.

A problem where you find the square-root of a number.

17.

The objective when solving an equation is to....

isolate the variable.

check the solution.

guess and check.

combine Like Terms.

18.

x - 62 = 123
How should you show your work to isolate the variable and solve the equation?

Add 62 to each side.

Subtract 62 from each side.

Multiply each side by 62.

Add 123 to each side.

19.

What is the inverse operation needed to solve for p?
765 = p - 254

subtraction

addition

multiplication

division

20.

What is the next step to solve this equation?
3x - 5 = 7

Add 5 to both sides of the equation

Add 3x to both sides of the equation

Subtract 5 from both sides of the equation

Subtract 7 from both sides of the equation

21.

What is the next step to solve this equation?
n - 4 = -2

Add 4 to both sides of the equation

Add n to both sides of the equation

Subtract n from both sides of the equation

Subtract 4 from both sides of the equation

22.

What is the next step to solve this equation?
5k + 6 = -9

Add 9 to both sides of the equation

Add 6 to both sides of the equation

Subtract 6 from both sides of the equation

Subtract 5k from both sides of the equation

23.

How would you solve the equation 9x = 153 ?

multiply both sides by 9

divide both sides by 9

add 9 to both sides

subtract 9 from both sides

24.

Which equation has a = 5 as the solution?

a + 15 = 10

2a = 5

2a = 10

a - 15 = 10

25.

x - 62 = 123
How should you show your work to solve the equation?

Add 62 to each side.

Subtract 62 from each side.

Multiply each side by 62.

Add 123 to each side.

26.

The steps in solving 5b - 6 = 24 are:

Add 6 to both sides and then divide both sides by 5

Add 6 to both sides and then multiply both sides by 5

Subtract 6 from both sides and then multiply both sides by 5

Subtract 6 from both sides and then divide both sides by 5

27.

What is the first step in solving this equation:
5x + 7 = 12

Divide by 5

Subtract 5

Multiply by 7

Subtract 7

28.

What is the first step in solving the following equation?

\frac{d}{6}=-3

Add 6 to both sides of the equal sign.

Subtract 6 from both sides of the equal sign.

Multiply by 6 to both sides of the equal sign.

Divide by 6 to both sides of the equal sign.

29.

What is the first step in solving the following equation?

8j = -16

Add 8 to both sides of the equal sign.

Subtract 8 from both sides of the equal sign.

Multiply by 8 to both sides of the equal sign.

Divide by 8 to both sides of the equal sign.

30.

What is the first step in solving the following equation?

-15 = 5b

Add 5 to both sides of the equal sign.

Subtract 5 from both sides of the equal sign.

Multiply by 5 to both sides of the equal sign.

Divide by 5 to both sides of the equal sign.

31.

What's the first step in solving the following:
-4x + 1 = 21

Add 1 to both sides

Subtract 1 from both sides

Multiply both sides by 1

Divide both sides by 1

32.

What's the second step in solving the following:
-4x + 1 = 21

Add -4 to both sides

Subtract -4 from both sides

Multiply both sides by -4

Divide both sides by -4

33.

What's the second step in solving the following:

\frac{x}{2}-5=3

Add 2 to both sides

Subtract 2 from both sides

Multiply both sides by 2

Divide both sides by 2

34.

In the expression 3m + 8, the number 3 is called the ____________.

variable

constant

coefficient

answer

35.

In the expression 3m + 8, the number 8 is called the ____________.

constant

variable

coefficient

answer

36.

What is the first step in solving for w in the equation 3w + 5 = 14?

Add 5 to both sides of the equal sign

Divide by 3 on both sides of the equal sign

Subtract 5 from both sides of the equal sign

Multiply by 3 on both sides of the equal sign

37.

In the equation 4c + 8 = 14, c is the ______________.

constant

coefficient

calculation

variable

38.

What do you have to do to both sides to solve the following equation: $5x\ =\ 55$

add 5 to both sides

subtract 5 from both sides

multiply both sides by 5

divide both sides by 5

39.

What do you have to do to both sides to solve the following equation: $-9\ +\ x\ =\ -21$

add 9 to both sides

subtract 9 from both sides

multiply both sides by 9

divide both sides by 9

40.

What do you have to do to both sides to solve the following equation: $\frac{x}{3}=13$

add 3 to both sides

subtract 3 from both sides

multiply both sides by 3

divide both sides by 3

41.

What do you have to do to both sides to solve the following equation: $\frac{3}{4}x\ =15$

add $\frac{3}{4}$ to both sides

subtract $\frac{3}{4}$ from both sides

multiply both sides by $\frac{4}{3}$

divide both sides by $\frac{4}{3}$

42.

What is the first step to solve this equation:
-11 - 3x = 44

Add 3 to both sides

Subtract 11 from both sides

Add 11 to both sides

Divide 3 on both sides.

43.

True or False: In order to solve the equation below, you would add 6 to each side and then multiply by -8 on each side.

\frac{g}{-8}\ -6\ =\ -12

True

False

44.

How would you solve the equation?
38 = m - 15

Subtract 15 from both sides

Add 15 to both sides

Multiply both sides by 15

Divide both sides by 15

45.

How would you solve the equation?

3\ =\frac{d}{17}

Divide both sides by 17

Add 3 to both sides

Multiply both sides by 3

Multiply both sides by 17

46.

To solve an equation, the goal is to __________ the variable on one side.

evaluate

reciprocal

isolate

algebra

47.

A letter or symbol that represents an unknown value is called ______________.

variable

radicand

coefficient

constant

48.

When you add a number to each side of an equation, you are using the ___________.

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

49.

A value that when substituted for the variable will make an equation true is a ____________.

Term

Constant

Evaluation

Solution

50.

What is the first step in solving the following equation?

\frac{r}{-7}=4

Add -7 to both sides of the equal sign.

Subtract -7 to both sides of the equal sign.

Multiply -7 to both sides of the equal sign.

Divide -7 to both sides of the equal sign.

Reset

#060 Solving & Setting Up Equations

Total questions: 50

Worksheet time: 40mins

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