SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES WORKSHEET

About "Solving equations with variables on both sides worksheet"

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.

Solving equations with variables on both sides worksheet - Problems

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 ?

Solving equations with variables on both sides worksheet - Solution

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.

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