Solve the Inequality for m 10m+5(4m+8)>=7m-6-2m

$10 m + 5 (4 m + 8) \geq 7 m - 6 - 2 m$

Simplify $10 m + 5 (4 m + 8)$ .

Simplify each term.

Apply the distributive property.

$10 m + 5 (4 m) + 5 \cdot 8 \geq 7 m - 6 - 2 m$

Multiply $4$ by $5$ .

$10 m + 20 m + 5 \cdot 8 \geq 7 m - 6 - 2 m$

Multiply $5$ by $8$ .

$10 m + 20 m + 40 \geq 7 m - 6 - 2 m$

Add $10 m$ and $20 m$ .

$30 m + 40 \geq 7 m - 6 - 2 m$

Subtract $2 m$ from $7 m$ .

$30 m + 40 \geq 5 m - 6$

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

Subtract $5 m$ from both sides of the inequality.

$30 m + 40 - 5 m \geq - 6$

Subtract $5 m$ from $30 m$ .

$25 m + 40 \geq - 6$

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

Subtract $40$ from both sides of the inequality.

$25 m \geq - 6 - 40$

Subtract $40$ from $- 6$ .

$25 m \geq - 46$

Divide each term in $25 m \geq - 46$ by $25$ and simplify.

Divide each term in $25 m \geq - 46$ by $25$ .

$\frac{25 m}{25} \geq \frac{- 46}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 m}{25} \geq \frac{- 46}{25}$

Divide $m$ by $1$ .

$m \geq \frac{- 46}{25}$

Simplify the right side.

Move the negative in front of the fraction.

$m \geq - \frac{46}{25}$

The result can be shown in multiple forms.

Inequality Form:

$m \geq - \frac{46}{25}$

Interval Notation:

$[- \frac{46}{25}, \infty)$