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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 2: Q 2.19 (page 107)

Solve $7 = \frac{1}{2} x + \frac{3}{4} x - \frac{2}{3} x$

Short Answer

Expert verified

The answer is $x = 12$

Step by step solution

01

Step 1. Given information

The equation is $7 = \frac{1}{2} x + \frac{3}{4} x - \frac{2}{3} x$

Find value of x.

02

Step 2. Calculation

Find LCD of denominators of equation $7 = \frac{1}{2} x + \frac{3}{4} x - \frac{2}{3} x$

LCD of 2,3,4 is 12

So

$7 \times 12 = 12 (\frac{1}{2} x + \frac{3}{4} x - \frac{2}{3} x)$

role="math" localid="1644248969105" $84 = 6 x + 9 x - 8 x$

Combine like terms

role="math" localid="1644249012482" $84 = 7 x \frac{84}{7} = x 12 = x$

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