Solved on Nov 07, 2023

Solve the equation $\frac{1}{2}(2 m-8)=6\left(\frac{1}{2} m+10\right)$ to find the possible values of $m$ .

STEP 1

Assumptions1. The given equation is $\frac{1}{}( m-8)=6\left(\frac{1}{} m+10\right)$ . We are looking for the value of $m$ that satisfies this equation.

STEP 2

First, we simplify both sides of the equation. We start with the left side by distributing the $\frac{1}{2}$ inside the parentheses.
$\frac{1}{2}(2 m-8) = m -4$

STEP 3

Next, we simplify the right side of the equation by distributing the6 inside the parentheses.
$6\left(\frac{1}{2} m+10\right) =3m +60$

STEP 4

Now, we rewrite the original equation with the simplified expressions.
$m -4 =3m +60$

STEP 5

To solve for $m$ , we need to isolate $m$ on one side of the equation. We can start by subtracting $3m$ from both sides to get rid of $3m$ on the right side.
$m -3m =3m -3m +60 +4$

STEP 6

implify the equation.
$-2m =64$

STEP 7

Finally, we divide both sides of the equation by -2 to solve for $m$ .
$m = \frac{64}{-2}$

STEP 8

Calculate the value of $m$ .
$m = -32$ So, the solution to the equation $\frac{1}{2}(2 m-8)=6\left(\frac{1}{2} m+10\right)$ is $m=-32$ .

Was this helpful?

Solve the equation $\frac{1}{2}(2 m-8)=6\left(\frac{1}{2} m+10\right)$ to find the possible values of $m$ .

STEP 1

Assumptions1. The given equation is $\frac{1}{}( m-8)=6\left(\frac{1}{} m+10\right)$ . We are looking for the value of $m$ that satisfies this equation.

STEP 2

First, we simplify both sides of the equation. We start with the left side by distributing the $\frac{1}{2}$ inside the parentheses.
$\frac{1}{2}(2 m-8) = m -4$

STEP 3

Next, we simplify the right side of the equation by distributing the6 inside the parentheses.
$6\left(\frac{1}{2} m+10\right) =3m +60$

STEP 4

Now, we rewrite the original equation with the simplified expressions.
$m -4 =3m +60$

STEP 5

To solve for $m$ , we need to isolate $m$ on one side of the equation. We can start by subtracting $3m$ from both sides to get rid of $3m$ on the right side.
$m -3m =3m -3m +60 +4$

STEP 6

implify the equation.
$-2m =64$

STEP 7

Finally, we divide both sides of the equation by -2 to solve for $m$ .
$m = \frac{64}{-2}$

STEP 8

Calculate the value of $m$ .
$m = -32$ So, the solution to the equation $\frac{1}{2}(2 m-8)=6\left(\frac{1}{2} m+10\right)$ is $m=-32$ .

Start learning now

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

Solve the equation 12(2m−8)=6(12m+10)\frac{1}{2}(2 m-8)=6\left(\frac{1}{2} m+10\right)21​(2m−8)=6(21​m+10) to find the possible values of mmm.

STEP 1

Assumptions1. The given equation is 1(m−8)=6(1m+10)\frac{1}{}( m-8)=6\left(\frac{1}{} m+10\right)1​(m−8)=6(1​m+10). We are looking for the value of mmm that satisfies this equation.

STEP 2

First, we simplify both sides of the equation. We start with the left side by distributing the 12\frac{1}{2}21​ inside the parentheses.12(2m−8)=m−4\frac{1}{2}(2 m-8) = m -421​(2m−8)=m−4

STEP 3

Next, we simplify the right side of the equation by distributing the6 inside the parentheses.6(12m+10)=3m+606\left(\frac{1}{2} m+10\right) =3m +606(21​m+10)=3m+60

STEP 4

Now, we rewrite the original equation with the simplified expressions.m−4=3m+60m -4 =3m +60m−4=3m+60

STEP 5

To solve for mmm, we need to isolate mmm on one side of the equation. We can start by subtracting 3m3m3m from both sides to get rid of 3m3m3m on the right side.m−3m=3m−3m+60+4m -3m =3m -3m +60 +4m−3m=3m−3m+60+4

STEP 6

implify the equation.−2m=64-2m =64−2m=64

STEP 7

Finally, we divide both sides of the equation by -2 to solve for mmm.m=64−2m = \frac{64}{-2}m=−264​

STEP 8

Calculate the value of mmm.m=−32m = -32m=−32So, the solution to the equation 12(2m−8)=6(12m+10)\frac{1}{2}(2 m-8)=6\left(\frac{1}{2} m+10\right)21​(2m−8)=6(21​m+10) is m=−32m=-32m=−32.

Start learning now

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

Solve the equation $\frac{1}{2}(2 m-8)=6\left(\frac{1}{2} m+10\right)$ to find the possible values of $m$ .

Assumptions1. The given equation is $\frac{1}{}( m-8)=6\left(\frac{1}{} m+10\right)$ . We are looking for the value of $m$ that satisfies this equation.

First, we simplify both sides of the equation. We start with the left side by distributing the $\frac{1}{2}$ inside the parentheses.
$\frac{1}{2}(2 m-8) = m -4$

Next, we simplify the right side of the equation by distributing the6 inside the parentheses.
$6\left(\frac{1}{2} m+10\right) =3m +60$

Now, we rewrite the original equation with the simplified expressions.
$m -4 =3m +60$

To solve for $m$ , we need to isolate $m$ on one side of the equation. We can start by subtracting $3m$ from both sides to get rid of $3m$ on the right side.
$m -3m =3m -3m +60 +4$

implify the equation.
$-2m =64$

Finally, we divide both sides of the equation by -2 to solve for $m$ .
$m = \frac{64}{-2}$

Calculate the value of $m$ .
$m = -32$ So, the solution to the equation $\frac{1}{2}(2 m-8)=6\left(\frac{1}{2} m+10\right)$ is $m=-32$ .