Question

Twice the sum of a number is 9 is equal to three times the difference of the number and 7

Answer 1

"Twice the sum of a number is 9 is equal to three times the difference of the number and 7" is our problem. Let's translate it into an equation.

Twice                                      2 times

the sum of a number           x +

and 9                                    9

is equal to                              =

three times                           3 times

the difference of a number x-

and 7                                      7

We move top down on the right side and make the equation. Then we solve it for x

2x + 9 = 3x - 7                           our equation

-x + 9 = -7                                    subtract 3x on both sides

-x = -16                                      subtract 16 on both sides

x = 16                                         divide both sides by -1

Thus the mystery number is 16.

Answer 2

First, write put the information into an equation

2*(x+9) = 3*(x-7)

distribute the 2 and 3
2x + 18 = 3x - 21

Combine like terms (Xs and munbers) (in this case, it's easier to add 15 to both sides and subtract 2x from both sides so both sides end up being positive)
33 = x

x=33