QuestionSolve the equation $3 x - \frac{1}{5} - \frac{2}{9} x = \frac{124}{5}$ . Simplify by combining like terms.

Studdy Solution

STEP 1

Assumptions1. The equation is $3x - \frac{1}{5} - \frac{}{9}x = \frac{124}{5}$ . We are solving for $x$

STEP 2

First, we need to combine like terms on the left side of the equation. The like terms are $x$ and $-\frac{2}{9}x$ .
$x - \frac{2}{9}x =x - \frac{2x}{9}$

STEP 3

To combine these terms, we need to have the same denominator. We can achieve this by multiplying $3x$ by $\frac{9}{9}$ .
$\frac{9}{9} \cdot3x - \frac{2x}{9} = \frac{27x}{9} - \frac{2x}{9}$

STEP 4

Now that we have the same denominator, we can subtract the numerators.
$\frac{27x -2x}{9} = \frac{25x}{9}$

STEP 5

Substitute this back into the original equation.
$\frac{25x}{9} - \frac{1}{5} = \frac{124}{5}$

STEP 6

To simplify further, we need to get rid of the fractions. We can do this by multiplying the entire equation by the least common multiple (LCM) of9 and5, which is45.
$45 \cdot \left(\frac{25x}{9} - \frac{1}{5}\right) =45 \cdot \frac{124}{5}$

STEP 7

istribute the45 on the left side of the equation.
$45 \cdot \frac{25x}{9} -45 \cdot \frac{1}{5} =45 \cdot \frac{124}{5}$

STEP 8

implify the multiplication.
$125x - =1116$

STEP 9

Add9 to both sides of the equation to isolate $x$ .
$125x =1116 +9$

STEP 10

implify the right side of the equation.
$125x =1125$

STEP 11

Finally, divide both sides of the equation by125 to solve for $x$ .
$x = \frac{1125}{125}$

STEP 12

implify the right side of the equation.
$x =9$ So, the solution to the equation is $x =9$ .

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