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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 2: Q 2.23 (page 109)

Solve $\frac{3 r + 5}{6} + 1 = \frac{4 r + 3}{3}$

Short Answer

Expert verified

The answer is $r = 1$

Step by step solution

01

Step 1. Given information

The equation is $\frac{3 r + 5}{6} + 1 = \frac{4 r + 3}{3}$

Find value of r and check it.

02

Step 2. Calculation

Simplify the equation $\frac{3 r + 5}{6} + 1 = \frac{4 r + 3}{3}$

LCD of 3,6 is 6. so,

$6 (\frac{3 r + 5}{6} + 1) = 6 (\frac{4 r + 3}{3}) 3 r + 5 + 6 = 8 r + 6$

Combine like terms,

$5 + 6 - 6 = 8 r - 3 r 5 = 5 r 1 = r$

03

Step 3. Check the answer

Substitute $r = 1$ in equation $\frac{3 r + 5}{6} + 1 = \frac{4 r + 3}{3}$

$\frac{3 (1) + 5}{6} + 1 = \frac{4 (1) + 3}{3} \frac{8}{6} + 1 = \frac{7}{3} \frac{7}{3} = \frac{7}{3}$

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