Question

Three times the sum of a number and 4 is 8 less than one-half the number. Write and solve equation to find the number.

Answer 1

Given

3 times the sum of a number and 4 is 8 less than half the number.

Find

an equation for the number

the number

Solution

Translating the given description to math symbols, we have

... 3(n +4) = -8 + n/2 . . . . . the equation

Eliminate parentheses

... 3n + 12 = -8 + n/2

... 3n = -20 + n/2 . . . . . . . subtract 12

... 2.5n = -20 . . . . . . . . . . subtract n/2

... n = -20/2.5 = -8 . . . . . divide by the coefficient of n

The number is -8.

_____

Check

3(-8+4) = -8 + (-8)/2

3(-4) = -8 -4

-12 = -12 . . . . . . . . . . . the answer works in the original problem

Answer 2

3(x+4)=(1/2)x-8 => 3x+12=(1/2)x-8 we will multiply equation with number 2 and we get 6x+12 = x-16 => 6x-x=-16-24 => 5x=-40 => x=-8

Good luck!!!