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QuestionSolve the equation x+616=98+x−63\frac{x+6}{16}=\frac{9}{8}+\frac{x-6}{3} and identify the solution set: A, B, or C.

Studdy Solution

STEP 1

Assumptions1. The given equation is a linear equation. . The equation is in the form of fractions.
3. We are looking for a solution set for the variable xx.

STEP 2

To solve the equation, we first need to eliminate the fractions. We can do this by finding the least common multiple (LCM) of the denominators (16,8, and) and multiplying each term by this value.
The LCM of16,8, and is48.
So, we multiply each term by48.
48⋅x+616=48⋅98+48⋅x−648 \cdot \frac{x+6}{16} =48 \cdot \frac{9}{8} +48 \cdot \frac{x-6}{}

STEP 3

Now, simplify each term.
3(x+6)=6⋅9+16(x−6)3(x+6) =6 \cdot9 +16(x-6)

STEP 4

Expand each term.
3x+18=54+16x−963x+18 =54 +16x -96

STEP 5

Rearrange the equation to bring all terms involving xx to one side and the constants to the other side.
3x−16x=54−18+963x -16x =54 -18 +96

STEP 6

implify the equation.
−13x=132-13x =132

STEP 7

To solve for xx, divide both sides of the equation by -13.
x=132−13x = \frac{132}{-13}

STEP 8

implify the right side to get the solution for xx.
x=−13213x = -\frac{132}{13}So, the solution set is {−13213}\{-\frac{132}{13}\}.

STEP 9

To check the solution, substitute x=−13213x = -\frac{132}{13} back into the original equation and simplify both sides. If both sides are equal, then the solution is correct.
Substitute x=−13213x = -\frac{132}{13} into the original equation−13213+616=98+−13213−63\frac{-\frac{132}{13}+6}{16}=\frac{9}{8}+\frac{-\frac{132}{13}-6}{3}

STEP 10

implify both sides of the equation.
After simplifying, if both sides of the equation are equal, then the solution is correct.

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