Exercise 31 Page 256

To solve the equation, we have to isolate j on one side. Using the Addition Property of Equality, we will add 12 to both sides of the equation. This will eliminate the subtraction and isolate j.

3/4 = j - 1/2

AddEqn

LHS+1/2=RHS+1/2

3/4 + 1/2 =j-1/2+1/2

AddFrac

Add fractions

3/4 + 1/2 =j

ExpandFrac

a/b=a * 2/b * 2

3/4 + 1 * 2/2 * 2 =j

Multiply

Multiply

3/4 +2/4 =j

AddFrac

Add fractions

5/4 = j

RearrangeEqn

Rearrange equation

j=5/4

To check that this solution is correct, let's substitute j= 54 into the original equation and simplify.

3/4 = j - 1/2

Substitute

j= 5/4

3/4 ? = 5/4 - 1/2

ExpandFrac

a/b=a * 2/b * 2

3/4 ? = 5/4 - 1* 2/2* 2

Multiply

Multiply

3/4 ? = 5/4 - 2/4

SubFrac

Subtract fractions

3/4 = 3/4 ✓

Since the left-hand side and right-hand side are equal, j= 54 is the correct solution.