Solved on Jan 13, 2024

Solve the linear equation $7(m-12)=5m$ for the value of $m$ .

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

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

STEP 8

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

STEP 9

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

STEP 10

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

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Solve the linear equation $7(m-12)=5m$ for the value of $m$ .

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

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

STEP 8

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

STEP 9

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

STEP 10

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

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Solve the linear equation 7(m−12)=5m7(m-12)=5m7(m−12)=5m for the value of mmm.

STEP 1

Assumptions1. We are given the equation 7(m−12)=5m7(m-12)=5m7(m−12)=5m.2. We need to solve for the variable mmm.

STEP 2

Distribute the 7 into the parentheses on the left side of the equation.7(m−12)=7m−7⋅127(m-12) = 7m - 7 \cdot 127(m−12)=7m−7⋅12

STEP 3

Calculate the multiplication within the parentheses.7m−7⋅12=7m−847m - 7 \cdot 12 = 7m - 847m−7⋅12=7m−84

STEP 4

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

STEP 5

To solve for mmm, we need to get all the terms with mmm on one side and the constant terms on the other. Start by subtracting 5m5m5m from both sides of the equation to move the terms with mmm to the left side.7m−5m−84=5m−5m7m - 5m - 84 = 5m - 5m7m−5m−84=5m−5m

STEP 6

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

STEP 7

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

STEP 8

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

STEP 9

To solve for mmm, divide both sides of the equation by 2.2m2=842\frac{2m}{2} = \frac{84}{2}22m​=284​

STEP 10

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

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the linear equation $7(m-12)=5m$ for the value of $m$ .

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

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

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

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

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

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

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

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

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

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