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QuestionSolve the equation −23(x+15)=−18(x+25)-\frac{2}{3}\left(x+\frac{1}{5}\right)=-\frac{1}{8}\left(x+\frac{2}{5}\right) and simplify.

Studdy Solution

STEP 1

Assumptions1. The equation given is −3(x+15)=−18(x+5)-\frac{}{3}\left(x+\frac{1}{5}\right)=-\frac{1}{8}\left(x+\frac{}{5}\right). We are asked to solve for xx
3. The solution should be expressed as an integer, a simplified fraction, or a decimal rounded to two decimal places

STEP 2

First, distribute the terms inside the parentheses on both sides of the equation.
−2x−215=−18x−120-\frac{2}{}x - \frac{2}{15} = -\frac{1}{8}x - \frac{1}{20}

STEP 3

Next, we want to isolate xx on one side of the equation. To do this, we can add 23x\frac{2}{3}x to both sides of the equation and add 120\frac{1}{20} to both sides of the equation.
−215+120=−18x+23x-\frac{2}{15} + \frac{1}{20} = -\frac{1}{8}x + \frac{2}{3}x

STEP 4

Now, simplify the right side of the equation by combining like terms.
−215+120=(23−18)x-\frac{2}{15} + \frac{1}{20} = \left(\frac{2}{3} - \frac{1}{8}\right)x

STEP 5

implify the left side of the equation by finding a common denominator and adding the fractions.
−8120+120=(23−18)x-\frac{8}{120} + \frac{}{120} = \left(\frac{2}{3} - \frac{1}{8}\right)x

STEP 6

implify the left side of the equation by subtracting the fractions.
−2120=(23−18)x-\frac{2}{120} = \left(\frac{2}{3} - \frac{1}{8}\right)x

STEP 7

implify the right side of the equation by finding a common denominator and subtracting the fractions.
−2120=(6424−324)x-\frac{2}{120} = \left(\frac{64}{24} - \frac{3}{24}\right)x

STEP 8

implify the right side of the equation by subtracting the fractions.
−2120=6124x-\frac{2}{120} = \frac{61}{24}x

STEP 9

Finally, to solve for xx, divide both sides of the equation by 6124\frac{61}{24}.
x=−2120÷6124x = -\frac{2}{120} \div \frac{61}{24}

STEP 10

implify the division on the right side of the equation by multiplying the numerator by the reciprocal of the denominator.
x=−2120×2461x = -\frac{2}{120} \times \frac{24}{61}

STEP 11

implify the multiplication on the right side of the equation.
x=−487320x = -\frac{48}{7320}

STEP 12

implify the fraction on the right side of the equation by dividing both the numerator and the denominator by their greatest common divisor, which is4.
x=−121830x = -\frac{12}{1830}The solution to the equation is x=−121830x = -\frac{12}{1830}.

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