Exercise 20 Page 131

To solve the equation, we have to isolate q on one side. Using the Subtraction Property of Equality, we will subtract 23 from both sides of the equation. This will eliminate the addition and isolate q.

1/2 = q + 2/3

SubEqn

LHS-2/3=RHS-2/3

1/2 - 2/3 = q + 2/3 - 2/3

SubFrac

Subtract fractions

1/2 - 2/3= q

▼

Simplify left-hand side

ExpandFrac

a/b=a * 3/b * 3

3/6 - 2/3 = q

ExpandFrac

a/b=a * 2/b * 2

3/6 - 4/6 = q

SubFrac

Subtract fractions

- 1/6 = q

RearrangeEqn

Rearrange equation

q = - 1/6

To check that this solution is correct, let's substitute q=- 16 into the original equation and simplify.

1/2 = q + 2/3

Substitute

q= - 1/6

1/2 ? = - 1/6 + 2/3

ExpandFrac

a/b=a * 2/b * 2

1/2 ? = - 1/6 + 4/6

AddTerms

Add terms

1/2 ? = 3/6

ReduceFrac

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

1/2 = 1/2 ✓

Since the left-hand side and right-hand side are equal, q=- 16 is the correct solution.