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Question Solve the linear equation −23(15x+3)=−3x−9-\frac{2}{3}(15 x+3)=-3 x-9 for the unknown variable xx.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation −23(15x+3)=−3x−9-\frac{2}{3}(15x+3)=-3x-9.
2. We need to solve for xx.

STEP 2

First, distribute the −23-\frac{2}{3} across the terms inside the parentheses.
−23(15x+3)=−23⋅15x−23⋅3-\frac{2}{3}(15x+3) = -\frac{2}{3} \cdot 15x - \frac{2}{3} \cdot 3

STEP 3

Multiply −23-\frac{2}{3} by 15x15x and 33 separately.
−23⋅15x=−10x-\frac{2}{3} \cdot 15x = -10x −23⋅3=−2-\frac{2}{3} \cdot 3 = -2

STEP 4

Substitute the results back into the equation.
−10x−2=−3x−9-10x - 2 = -3x - 9

STEP 5

Now, isolate the variable xx on one side of the equation. First, add 10x10x to both sides of the equation to move the xx terms to one side.
−10x−2+10x=−3x−9+10x-10x - 2 + 10x = -3x - 9 + 10x

STEP 6

Combine like terms on both sides of the equation.
−2=7x−9-2 = 7x - 9

STEP 7

Next, add 99 to both sides of the equation to move the constant terms to the other side.
−2+9=7x−9+9-2 + 9 = 7x - 9 + 9

STEP 8

Combine like terms on both sides of the equation.
7=7x7 = 7x

STEP 9

Finally, divide both sides of the equation by 77 to solve for xx.
77=7x7\frac{7}{7} = \frac{7x}{7}

STEP 10

Simplify both sides of the equation to find the value of xx.
1=x1 = x
The solution to the equation −23(15x+3)=−3x−9-\frac{2}{3}(15x+3)=-3x-9 is x=1x = 1.

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