USING MULTIPLICATION TO SOLVE EQUATIONS

Example 1 :

Solve the following equation and graph the solution on a number line.

x/5 = 10

Solution :

Since we are trying to solve for x, we have to get rid of 5 which divides x in the above equation.

To get rid of 5, we have to multiply both sides of the equation by 5.

(x/5) x 5 = 10 x 5

x = 50

Example 2 :

Solve the equation and and graph the solution on a number line.

15 = r/2

Solution :

15 = r/2

Multiply both sides by 2.

15 x 2 = (r/2) x 2

30 = r

Example 3 :

Solve the equation and graph the solution on a number line.

y/9 = 1

Solution :

y/9 = 1

Multiply both sides by 9.

(y/9) x 9 = 1 x 9

y = 9

Example 4 :

John had some candies. He shared the candies equally to his 3 kids. If each kid had received 7 candies, how many candies did John have ?

Solution :

Let m be the number of candies that John had initially.

m/3 = 7

Multiply both sides by 3 to solve for m.

(m/3) x 3 = 7 x 3

m = 21

Hence, John initially had 21 candies.

Example 5 :

The speed of John is 50 miles per hour. If he covers one-fifth of a certain distance in 2 hours, find the actual distance.

Solution :

Let d be the actual distance.

distance = speed x time

(1/5)d = 50 x 2

d/5 = 100

Multiply both sides by 5.

(d/5) x 5 = 100 x 5

d = 500

The actual distance is 500 miles.

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