Exercise 27 Page 9

To solve the equation, we have to isolate k on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by 10 and eliminate the denominators of the fractions. Now, we can use the Division Property of Equality to divide both sides of the equation by 9. This will eliminate the coefficient of k and isolate it on the right-hand side of the equation.

15=9k

DivEqn

.LHS /9.=.RHS /9.

15/9=9k/9

ReduceFrac

a/b=.a /3./.b /3.

5/3=9k/9

▼

Simplify right-hand side

ReduceFrac

a/b=.a /9./.b /9.

5/3=k/1

DivByOne

a/1=a

5/3=k

FracToMixed

Write fraction as a mixed number

1 23=k

RearrangeEqn

Rearrange equation

k=1 23

To check that this solution is correct, let's substitute k= 1 23 into the original equation and simplify.

3/2=9/10k

Substitute

k= 12/3

3/2? =9/10( 1 23)

▼

Simplify right-hand side

MixedToFrac

a bc=a* c+b/c

3/2? =9/10(1* 3+2/3)

Multiply

Multiply

3/2? =9/10(3+2/3)

AddTerms

Add terms

3/2? =9/10(5/3)

MultFrac

Multiply fractions

3/2? =9* 5/10* 3

Multiply

Multiply

3/2? =45/30

ReduceFrac

a/b=.a /15./.b /15.

3/2=3/2 ✓

Since the left-hand side and right-hand side are equal, k=1 23 is the correct solution.