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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 2: Q. 49 (page 112)

In the following exercises, solve each equation with fraction coefficients.
$2 = \frac{1}{3} x 鈭� \frac{1}{2} x + \frac{2}{3} x$

Short Answer

Expert verified

The value of $x = 4$

Step by step solution

01

Step 1. Given Information

In the given question we have to solve equation with fraction coefficients.

$2 = \frac{1}{3} x 鈭� \frac{1}{2} x + \frac{2}{3} x$

02

Step 2. The given equation is 2=13x−12x+23x

Now we solve the given equation for the value of $x$ .

03

Step 3. We want to clear the fractions by multiplying both sides of the equation by the LCD of all the fractions in the equation.

Finding the LCD of all fractions in the equation.

The numbers are $2, 3$

So the LCD is $6$

04

Step 4. Multiply both sides of the equation by 6.

$2 脳 6 = 6 (\frac{1}{3} x 鈭� \frac{1}{2} x + \frac{2}{3} x)$

Distribute.

$12 = 6 脳 \frac{1}{3} x 鈭� 6 脳 \frac{1}{2} x + 6 脳 \frac{2}{3} x 12 = 2 x 鈭� 3 x + 4 x$

Simplify鈥攏otice, no more fractions.

Combine like terms.

$12 = 3 x 3 x = 12$

Divide by $3$ on both side

$\frac{3}{3} x = \frac{12}{3} x = 4$

05

Step 5. Now checking the value.

Putting $x = 4$ in the given equation

$2 = \frac{1}{3} x 鈭� \frac{1}{2} x + \frac{2}{3} x 2 = \frac{1}{3} 脳 4 鈭� \frac{1}{2} 脳 4 + \frac{2}{3} 脳 4 2 = \frac{4}{3} 鈭� \frac{4}{2} + \frac{8}{3} 2 = \frac{4}{3} 脳 \frac{2}{2} 鈭� \frac{4}{2} 脳 \frac{3}{3} + \frac{8}{3} 脳 \frac{2}{2} 2 = \frac{8}{6} - \frac{12}{6} + \frac{16}{6} 2 = \frac{8 - 12 + 16}{6} 2 = \frac{12}{6} 2 = 2$

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