Solve the Inequality for m m+17<=-(4m-13)

$m + 17 \leq - (4 m - 13)$

Step 1

Simplify $- (4 m - 13)$ .

Rewrite.

$m + 17 \leq 0 + 0 - (4 m - 13)$

Simplify by adding zeros.

$m + 17 \leq - (4 m - 13)$

Apply the distributive property.

$m + 17 \leq - (4 m) - - 13$

Multiply.

Multiply $4$ by $- 1$ .

$m + 17 \leq - 4 m - - 13$

Multiply $- 1$ by $- 13$ .

$m + 17 \leq - 4 m + 13$

Step 2

Move all terms containing $m$ to the left side of the inequality.

Add $4 m$ to both sides of the inequality.

$m + 17 + 4 m \leq 13$

Add $m$ and $4 m$ .

$5 m + 17 \leq 13$

Step 3

Move all terms not containing $m$ to the right side of the inequality.

Subtract $17$ from both sides of the inequality.

$5 m \leq 13 - 17$

Subtract $17$ from $13$ .

$5 m \leq - 4$

Step 4

Divide each term in $5 m \leq - 4$ by $5$ and simplify.

Divide each term in $5 m \leq - 4$ by $5$ .

$\frac{5 m}{5} \leq \frac{- 4}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 m}{5} \leq \frac{- 4}{5}$

Divide $m$ by $1$ .

$m \leq \frac{- 4}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$m \leq - \frac{4}{5}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$m \leq - \frac{4}{5}$

Interval Notation:

$(- \infty, - \frac{4}{5}]$