Question

find the value of m: -2(m - 5) = -4
m = 7
m = 3
m = -3
m = -7

Explanation:

Step1: Divide both sides by -2

To isolate the term with \( m \), we divide both sides of the equation \(-2(m - 5) = -4\) by \(-2\).
\[
\frac{-2(m - 5)}{-2} = \frac{-4}{-2}
\]
Simplifying both sides, we get \( m - 5 = 2 \).

Step2: Add 5 to both sides

To solve for \( m \), we add 5 to both sides of the equation \( m - 5 = 2 \).
\[
m - 5 + 5 = 2 + 5
\]
Simplifying both sides, we find \( m = 7 \). Wait, no, wait. Wait, \(\frac{-4}{-2}\) is 2? Wait, no, \(-4\) divided by \(-2\) is 2? Wait, no, let's re - check. Wait, the original equation is \(-2(m - 5)=-4\). Dividing both sides by \(-2\): \(m - 5=\frac{-4}{-2}=2\). Then adding 5 to both sides: \(m=2 + 5=7\)? But wait, let's substitute back. If \(m = 7\), then \(-2(7 - 5)=-2\times2=-4\), which matches the right - hand side. Wait, but let's check the other way. Wait, maybe I made a mistake in the first step. Wait, let's do it again.

Starting over:

Step1: Distribute -2

First, we use the distributive property \(a(b - c)=ab - ac\) on the left - hand side of the equation \(-2(m - 5)=-4\). So, \(-2\times m-(-2)\times5=-4\), which simplifies to \(-2m + 10=-4\).

Step2: Subtract 10 from both sides

Subtract 10 from both sides of the equation \(-2m+10 = - 4\): \(-2m+10 - 10=-4 - 10\). This gives \(-2m=-14\).

Step3: Divide both sides by -2

Divide both sides of the equation \(-2m=-14\) by \(-2\): \(\frac{-2m}{-2}=\frac{-14}{-2}\). So, \(m = 7\).

Wait, but when we substitute \(m = 7\) into the original equation \(-2(7 - 5)=-2\times2=-4\), which is correct. But let's check the option \(m = 3\). If \(m = 3\), then \(-2(3 - 5)=-2\times(-2)=4
eq - 4\). If \(m=-3\), \(-2(-3 - 5)=-2\times(-8)=16
eq - 4\). If \(m=-7\), \(-2(-7 - 5)=-2\times(-12)=24
eq - 4\). So the correct value of \(m\) is 7.

Answer:

\(m = 7\) (corresponding to the option "m = 7")