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 2.3 - Solving Linear Equations - Exercise Set - Page 142: 85

Answer

The equation we found was $\frac{3}{4}x - 3 = \frac{1}{2}x$. $$x = 12$$

Work Step by Step

Let us translate this statement into an algebraic equation we can solve. "$3$ is subtracted from three-fourths of a number" means: $$\frac{3}{4}x - 3$$ The result of this expression is equal to "one-half of the number" means: $$ = \frac{1}{2}x$$ We already have both sides of the equation, so let us put them together: $$\frac{3}{4}x - 3 = \frac{1}{2}x$$ Now, we can solve for $x$ to find that unknown number: Add $3$ to both sides of the equation to get the constant on one side of the equation first: $$\frac{3}{4}x = \frac{1}{2}x + 3$$ Now, subtract $\frac{1}{2}x$ to isolate variables to the other side of the equation: $$\frac{3}{4}x - \frac{1}{2}x = 3$$ To subtract fractions, we need to find the lowest common denominator of the two fractions. In this case, the lowest common denominator is $4$, so we multiply the terms on both sides of the equation by $4$ to get rid of the fractions: $$4(\frac{3}{4}x) - 4(\frac{1}{2}x) = 4(3)$$ Divide out common factors to get rid of the fractions: $$3x - 2x = 4(3)$$ Multiply on the right-hand side to simplify: $$3x - 2x = 12$$ Subtract to solve for $x$: $$x = 12$$
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