Solve for m.

1+5m>

3m–19+13m
Write your answer using a decimal, whole number, or fraction in lowest terms.

1 answer

To solve the inequality \( 1 + 5m > -3m - 19 + 13m \), we first simplify the right-hand side.

Combine like terms on the right:

\[ -3m + 13m = 10m \]

This gives:

\[ 1 + 5m > 10m - 19 \]

Next, let's isolate \( m \). First, subtract \( 5m \) from both sides:

\[ 1 > 10m - 5m - 19 \]

This simplifies to:

\[ 1 > 5m - 19 \]

Now, add \( 19 \) to both sides to isolate the term with \( m \):

\[ 1 + 19 > 5m \]

This simplifies to:

\[ 20 > 5m \]

Now, divide both sides by \( 5 \):

\[ \frac{20}{5} > m \]

Which simplifies to:

\[ 4 > m \]

Or, written in a more standard form:

\[ m < 4 \]

Thus, the solution is:

\[ m < 4 \]