Solve the equation. What is the value of m?

Question

One way you can start solving is to make sure there are only m terms on one side. What move can you make to both sides of the equation to get rid of the
3
2
​
m on the left, while keeping the equation balanced?
3
2
​
m + 5
=
m + 15

Multiply both sides by
3
2
​
m

Divide both sides by
3
2
​
m

Add
3
2
​
m to both
sides

Subtract
3
2
​
m from both
sides
Good work!
You can subtract
3
2
​
m from the left side of the equation, so that the m terms are only on the right side of the equation, while keeping the equation balanced. Record subtracting
3
2
​
m from both sides now.
3
2
​
m + 5
=
m + 15
−

3
2
​
m
−

3
2
​
m
Great job!
We have m terms on both sides of the equation, and we want to get the m terms on one side. We can subtract
3
2
​
m on the left side of the equation so that there are no m terms on the left. Then we need to subtract
3
2
​
m from the right to keep the equation balanced. Go for it.
3
2
​
m + 5
=
m + 15
−
3
2
​
m
−
3
2
​
m

=

Answer 1

Let's solve the equation step by step following the moves you mentioned.

The original equation is:

\[ \frac{3}{2}m + 5 = m + 15 \]

You want to subtract \(\frac{3}{2}m\) from both sides:

\[ \frac{3}{2}m + 5 - \frac{3}{2}m = m + 15 - \frac{3}{2}m \]

This simplifies to:

\[ 5 = m + 15 - \frac{3}{2}m \]

Now let's combine the \(m\) terms on the right side. We can rewrite \(m\) as \(\frac{2}{2}m\):

\[ 5 = \frac{2}{2}m + 15 - \frac{3}{2}m \]

Now combine the \(m\) terms:

\[ 5 = ( \frac{2}{2}m - \frac{3}{2}m ) + 15 \] \[ 5 = -\frac{1}{2}m + 15 \]

Next, we've got \(15\) on the right. Let's isolate the \(-\frac{1}{2}m\) term by subtracting \(15\) from both sides:

\[ 5 - 15 = -\frac{1}{2}m \]

This simplifies to:

\[ -10 = -\frac{1}{2}m \]

Now, to eliminate the negative sign, multiply both sides by \(-1\):

\[ 10 = \frac{1}{2}m \]

Next, multiply both sides by \(2\) to solve for \(m\):

\[ 2 \cdot 10 = m \]

Thus,

\[ m = 20 \]

So, the value of \(m\) is:

\[ \boxed{20} \]