Problem

Write the following as an equation. Then solve.EXAMPLE 1Finding an Unknown NumberTwice a n...

Write the following as an equation. Then solve.

EXAMPLE 1

Finding an Unknown Number

Twice a number, added to seven, is the same as three subtracted from the number. Find the number.

Solution

Translate the sentence into an equation and solve.

To solve, begin by subtracting x from both sides to get all variable terms on one side.

Check the solution in the problem as it was originally stated. To do so, replace “number” in the sentence with −10. Twice “ −10 ” added to 7 is the same as 3 subtracted from “−10. ”

The unknown number is −10.

EXAMPLE 2

Finding an Unknown Number

Twice the sum of a number and 4 is the same as four times the number, decreased by 12. Find the number.

Solution

1. UNDERSTAND. Read and reread the problem. If we let
x = the unknown number, then
“the sum of a number and 4” translates to “x + 4” and “four times the number” translates to “4x.”
2. TRANSLATE.
3. SOLVE.
4. INTERPRET.
Check: Check this solution in the problem as it was originally stated. To do so, replace “number” with 10. Twice the sum of “10” and 4 is 28, which is the same as 4 times “10” decreased by 12.
State: The number is 10.