# 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.

**Q5: **

Given that , find .

**Q6: **

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

- A , ,
- B , ,
- C , ,
- D , ,
- E , ,

**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

**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

**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?