Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 2 - Section 2.4 - Formulas and Percents - Exercise Set - Page 155: 85

Answer

The solution is: $$y = 20$$ To determine if the solution is correct, we plug $20$ in for $y$ into the equation to see if both sides of the equation are equal: $$5(2(20) - 3) - 1 = 4(6 + 2(20))$$ We can simplify what we have in parentheses: $$5(40 - 3) - 1 = 4(6 + 40)$$ $$5(37) - 1 = 4(46)$$ We simplify using order of operations to multiply first: $$185 - 1 = 184$$ We then do the subtraction: $$184 = 184$$ We see that the solution is correct because both sides of the equation are equal.

Work Step by Step

To solve, we have to simplify the equation first. We distribute the terms in parentheses: $$10y - 15 - 1 = 24 + 8y$$ We now move the $y$ terms to one side of the equation by subtracting $8y$ from both sides of the equation: $$2y - 15 - 1 = 24$$ We want constants on the other side of the equation, so we add both $15$ and $1$ to both sides of the equation: $$2y = 40$$ We now isolate $y$ by dividing both sides by $2$: $$y = 20$$ To determine if the solution is correct, we plug $20$ in for $y$ into the equation to see if both sides of the equation are equal: $$5(2(20) - 3) - 1 = 4(6 + 2(20))$$ We can simplify what we have in parentheses: $$5(40 - 3) - 1 = 4(6 + 40)$$ $$5(37) - 1 = 4(46)$$ We simplify using order of operations to multiply first: $$185 - 1 = 184$$ We then do the subtraction: $$184 = 184$$ We see that the solution is correct because both sides of the equation are equal.
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