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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 2: Q 2.24 (page 97)

Solve $\frac{2 s + 3}{2} + 1 = \frac{3 s + 2}{4}$

Short Answer

Expert verified

The answer is $s = - 8$

Step by step solution

01

Step 1. Given Information

The equation is $\frac{2 s + 3}{2} + 1 = \frac{3 s + 2}{4}$

Find value of s and check it

02

Step 2. Calculation

Simplify the equation $\frac{2 s + 3}{2} + 1 = \frac{3 s + 2}{4}$

LCD of 2 and 4 is 4. So,

$4 (\frac{2 s + 3}{2} + 1) = 4 (\frac{3 s + 2}{4})$

The equation becomes, $4 s + 6 + 4 = 3 s + 2$

Combine like terms

$4 s - 3 s = 2 - 10 s = - 8$

03

Step 3. Check

Substitute $s = - 8$ in $\frac{2 s + 3}{2} + 1 = \frac{3 s + 2}{4}$

$\frac{2 (- 8) + 3}{2} + 1 = \frac{3 (- 8) + 2}{4} \frac{- 11}{2} = \frac{- 11}{2}$

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