Math

Question Solve the linear equation 7(m12)=5m7(m-12)=5m for the value of mm.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation 7(m12)=5m7(m-12)=5m.
2. We need to solve for the variable mm.

STEP 2

Distribute the 7 into the parentheses on the left side of the equation.
7(m12)=7m7127(m-12) = 7m - 7 \cdot 12

STEP 3

Calculate the multiplication within the parentheses.
7m712=7m847m - 7 \cdot 12 = 7m - 84

STEP 4

Rewrite the equation with the distributed terms.
7m84=5m7m - 84 = 5m

STEP 5

To solve for mm, we need to get all the terms with mm on one side and the constant terms on the other. Start by subtracting 5m5m from both sides of the equation to move the terms with mm to the left side.
7m5m84=5m5m7m - 5m - 84 = 5m - 5m

STEP 6

Simplify both sides of the equation by combining like terms.
2m84=02m - 84 = 0

STEP 7

Now, add 84 to both sides of the equation to isolate the term with mm on one side.
2m84+84=0+842m - 84 + 84 = 0 + 84

STEP 8

Simplify both sides of the equation.
2m=842m = 84

STEP 9

To solve for mm, divide both sides of the equation by 2.
2m2=842\frac{2m}{2} = \frac{84}{2}

STEP 10

Calculate the division to find the value of mm.
m=42m = 42
The solution to the equation 7(m12)=5m7(m-12)=5m is m=42m = 42.

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