Solve Equations using the Division and Multiplication Properties of Equality: example 2.16

Solve: $\frac{3}{4} x = 12 .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve: $\frac{2}{5} n = 14 .$

How did it go?


Multiply by the reciprocal of $\frac{3}{4}$ .
Reciprocals multiply to 1.
Multiply.
Notice that we could have divided both sides of the equation $\frac{3}{4} x = 12$ by $\frac{3}{4}$ to isolate $x$ . While this would work, most people would find multiplying by the reciprocal easier.
Check:
Substitute $x = 16$ .


Multiply by the reciprocal of $\frac{3}{4}$ .
Reciprocals multiply to 1.
Multiply.
Notice that we could have divided both sides of the equation $\frac{3}{4} x = 12$ by $\frac{3}{4}$ to isolate $x$ . While this would work, most people would find multiplying by the reciprocal easier.
Check:
Substitute $x = 16$ .