Question

Five less than twice the value of a number is equal to three times the quantity of

four more than one-half the number. What is the
number?
a. Let x be the number. Write and solve an equation to find x. Show your work.
b. Does the solution of your equation solve the original problem? Explain.

Answer 1

These types of questions are not daunting if you break it down. First look at "Five less than twice the value of a number."

"Twice the value of a number" is simply 2x.

"Five less" is simply -5, so for the first part we have (2x-5)

Next, analyze the second part. "Three times the quantity of four more than one half the number."

Looking at "Three times the quantity" simply means "3 times something".

"the quantity of four more than one half the number" is 4 + "one half the number" or 4 + (1/2)x.

So the second part is simply 3(4+x/2).

Finally we finish the entire equation, (2x-5) = 3(4+x/2) then solve for x.

2x-5 = 12 + (3/2)x

2x-(3/2)x = 17

x/2 = 17

x=34

Checking the left side, (2x-5) = 2(34) - 5 = 63.

Checking the right side, 3(4+(34/2)) = 3(4+17) = 3(21) = 63.