**Solving equations with variables on both sides worksheet :**

Worksheet on solving equations with variables on both sides is much useful to the students who would like to practice solving word problems on linear equations.

1. Solve for x : 3x - 1 = x + 5

2. David's Rental Car charges an initial fee of $20 plus an additional $30 per day to rent a car. Alex's Rental Car charges an initial fee of $36 plus an additional $28 per day. For what number of days is the total cost charged by both of them the same ?

**Problem 1 :**

Solve for x :

3x - 1 = x + 5

**Solution : **

**Step 1 : **

To get rid of "x" on the right side, we have to subtract "x" on both sides.

aaaaaaaaaaaaaaaaaaaa3x - 1 = x + 5 aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa -x -x aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa---------------- aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa 2x - 1 = 5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa----------------

**Step 2 : **

To get rid "-1", add "1" to both sides of the equation.

aaaaaaaaaaaaaaaaaaaa2x - 1 = 5 aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaa + 1 = +1 aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa-------------- aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa 2x = 6 aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa--------------

**Step 3 : **

To get rid of "2" multiplied by x, divide by 2 on both sides.

2x / 2 = 6 / 2

x = 3

**Problem 2 :**

David's Rental Car charges an initial fee of $20 plus an additional $30 per day to rent a car. Alex's Rental Car charges an initial fee of $36 plus an additional $28 per day. For what number of days is the total cost charged by both of them the same ?

**Solution : **

**Let "x" be the number of days for which the total cost charged by both of them is same.**

**Step 1 : **

Write an expression using "x" representing the total cost of renting a car from David’s Rental Car.

Total cost = Initial fee + cost for "x" days

Total days = 20 + 30x

**Step 2 : **

Write an expression using "x" representing the total cost of renting a car from Alex’s Rental Car.

Total cost = Initial fee + cost for "x" days

Total days = 36 + 28x

**Step 3 : **

We have assumed that the total cost charged by both of them is same for "x" number of days.

So, we have

20 + 30x = 36 + 28x

**Step 4 : **

To get rid of "28x" on the right side, we have to subtract "28x" from both sides.

aaaaaaaaaaaaaaaaaa20 + 30x = 36 + 28x aaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa -28x -28x aaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa------------------------aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa 20 + 2x = 36 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa------------------------

**Step 5 : **

To get rid of "20" on the left side, subtract 20 from both sides.

aaaaaaaaaaaaaaaaaaaaa20 + 2x = 36 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa -20 -20 aaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa----------------aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa 2x = 16 aaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa ----------------

**Step 6 : **

To get rid of "2" multiplied by x, divide by 2 on both sides.

2x / 2 = 16 / 2

x = 8

Hence, the total cost charged by both of them is same for 8 days.

After having gone through the stuff given above, we hope that the students would have understood "Solving equations with variables on both sides worksheet".

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