Question19 3 15 2-3x = 30 ct answer: x = logi (10)) mation or

Studdy Solution

STEP 1

1. The equation is $\frac{19}{3} + \frac{15}{2 - 3x} = 30$ .
2. We will solve for $x$ by isolating the variable.

STEP 2

1. Isolate the term with the variable $x$ .
2. Solve for $x$ .

STEP 3

First, subtract $\frac{19}{3}$ from both sides to isolate the term with the variable:
$\frac{15}{2 - 3x} = 30 - \frac{19}{3}$
To simplify the right side, find a common denominator:
$30 = \frac{90}{3}$
Thus:
$30 - \frac{19}{3} = \frac{90}{3} - \frac{19}{3} = \frac{71}{3}$
Now the equation is:
$\frac{15}{2 - 3x} = \frac{71}{3}$

STEP 4

To solve for $x$ , cross-multiply to eliminate the fractions:
$15 \cdot 3 = 71 \cdot (2 - 3x)$
Simplify both sides:
$45 = 71 \cdot 2 - 71 \cdot 3x$
$45 = 142 - 213x$
Rearrange to solve for $x$ :
$213x = 142 - 45$
$213x = 97$
Divide both sides by 213:
$x = \frac{97}{213}$
The value of $x$ is:
$\boxed{\frac{97}{213}}$

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