# Worksheet: Solving Equations with Rational Numbers

In this worksheet, we will practice solving equations involving rational numbers by finding the solution set of a given linear equation.

Q1:

Determine the value of , given that .

• A
• B
• C
• D

Q2:

If , then find the value of .

Q3:

Solve .

• A
• B
• C
• D
• E5

Q4:

.

• A
• B
• C
• D

Q5:

.

• A4
• B12
• C1
• D2

Q6:

If the number of eggs in a basket is 4 eggs, then the whole basket has eggs.

Q7:

Which of the following equations is equivalent to

• A
• B
• C
• D
• E

Q8:

.

• A
• B
• C
• D

Q9:

.

• A3
• B2
• C22
• D42

Q10:

Fill in the blanks.

• A8, 8, 9
• B10, 9, 9
• C8, 9, 10
• D8, 8, 10

Q11:

A truck traveled 220 miles in hours. On average, how many miles per hour did it travel?

• A mph
• B30 mph
• C660 mph
• D mph
• E mph

Q12:

Jacob drove for hours at 79 miles per hour. About how many miles did he drive?

Q13:

Solve the following equation: .

• A
• B
• C
• D
• E

Q14:

Two students tried to solve the equation . The first student added to both sides, while the second subtracted from both sides. Determine which student was correct, and then solve for the variable.

• Athe second student,
• Bthe second student,
• Cthe first student,
• Dthe first student,

Q15:

When is added to , the answer is 0. What is the value of ?

• A
• B
• C
• D
• E

Q16:

Solve for .

• A
• B5
• C
• D
• E

Q17:

Charlotte rode the bus to work today. She traveled miles and, due to bad traffic, it took of an hour. Solve the equation to find the average speed, , of the bus.

• A mph
• B mph
• C mph
• D mph
• E mph

Q18:

Which of the following equations is equivalent to

• A
• B
• C
• D
• E

Q19:

Find the rational number that equals 8 if is subtracted from it.

Q20:

Find the value of given .

Q21:

Solve .

• A
• B
• C
• D
• E

Q22:

Find the rational number that when subtracted from its additive inverse gives .

• A
• B
• C
• D

Q23:

Find given is the additive inverse of .

• A
• B
• C
• D
• E

Q24:

Solve for .

• A
• B
• C
• D
• E

Q25:

Noah spends 2 hours doing homework every night. On Monday, he spent ten minutes doing geography research. The rest of his time was split so that he spent twice as long on math homework as he did on his reading, and he spent the same amount of time on an essay as he did on math.

Write an equation that can be used to determine , the amount of time that he spent doing his math homework on Monday.

• A
• B
• C
• D
• E