# Worksheet: Linear Equations with Variables on Both Sides

In this worksheet, we will practice solving equations in which the variable is on each side of the equation.

Q1:

Find the value of :

Q2:

Solve the equation .

• A
• B
• C
• D

Q3:

Find the value of in .

Q4:

Solve the equation .

• A
• B
• C
• D

Q5:

Given that , find .

Q6:

If is isosceles, where , , , and , find the length of each side.

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q7:

is a rectangle where and . Find .

Q8:

Find the value of .

Q9:

Find the value of :

Q10:

Find the value of :

Q11:

Find the value of :

• A
• B
• C
• D
• E

Q12:

Find the value of in .

Q13:

Find the solution set of the equation .

• A
• B
• C
• D

Q14:

Find the solution set of the equation .

• A
• B
• C
• D

Q15:

Given that , use the information in the figure to find the perimeter of triangle .

Q16:

Mason and Jacob are going on vacation together. Mason has \$400 and Jacob has \$350. Given that, on average, Mason spends \$28 and Jacob spends \$26 per day, after how many days will they have the same amount of money left?

• A25 days
• B15 days
• C50 days
• D30 days
• E13 days

Q17:

80 students decided to buy a present for their teacher. They split into two groups of 40. In the first group, each student gave dollars. In the second group, three-fifths of the students gave dollars each, and the rest contributed a total of \$288. Given that the two groups contributed the same amount, find the value of .

• A20
• B36
• C16
• D26
• E12

Q18:

Find the value of given the following information:

• is on the line between and .
• .
• .
• .

Q19:

Point is the midpoint of segment . Given that the length of is , and that of is , what is the length of ?

Q20:

Solve .

• A
• B
• C
• DThere is an infinite number of solutions as the equation is always true.
• EThere is no solution for

Q21:

Find the value of in the equation .

• A
• B
• C
• D
• E2

Q22:

The startup cost for a restaurant is , and each meal costs \$10 for the restaurant to make. If each meal is then sold for \$15, after how many meals does the restaurant break even?

Q23:

Solve .

• A
• B
• C
• DThere is no solution for .
• E

Q24:

Solve .

• A
• B
• C
• D
• E

Q25:

What is the value of if the equation has no solutions?