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

a) x = 34

b) yes, it checks out

Explanation:

2x - 5 = 3(4 + 1/2x)

multiply both sides by 2 to eliminate fraction

2[2x - 5 = 3(4 + 1/2x)] = 4x - 10 = 24 + 3x

x - 10 = 24

x = 34

check

2(34) - 5 = 3(4 + 34/2)

68 - 5 = 3(4 + 17)

63 = 3(21)

63 = 63