Exercise 7 Page 388

We will solve the equation by isolating x on one side. We can use the Division Property of Equality to divide both sides of the equation by 8. This will eliminate the multiplication and isolate x. Let's do it!

8x = 72

DivEqn

.LHS /8.=.RHS /8.

8x/8 = 72/8

MovePartNumRight

a* b/c=a/c* b

8/8x = 72/8

QuotOne

a/a=1

1x = 72/8

IdPropMult

Identity Property of Multiplication

x = 72/8

CalcQuot

Calculate quotient

x = 9

Now we want to check our answer and make sure our solution is correct. Let's substitute x=9 into the original equation and simplify.

8x = 72

Substitute

x= 9

8 ( 9) ? = 72

Multiply

Multiply

72=72 ✓

Since the left-hand side and right-hand side are equal, x=9 is the correct solution.

Extra

Properties of Equality

There are four main Properties of Equality that we use when solving linear equations.

Properties of Equality
Addition Property of Equality	If a=b, then a+c=b+c.
Subtraction Property of Equality	If a=b, then a-c=b-c.
Multiplication Property of Equality	If a=b, then ac=bc.
Division Property of Equality	If a=b and c is not 0, then ac= bc.