Solve the Inequality for m -10m+8<=10m-2

$- 10 m + 8 \leq 10 m - 2$

Step 1

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

Subtract $10 m$ from both sides of the inequality.

$- 10 m + 8 - 10 m \leq - 2$

Subtract $10 m$ from $- 10 m$ .

$- 20 m + 8 \leq - 2$

Step 2

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

Subtract $8$ from both sides of the inequality.

$- 20 m \leq - 2 - 8$

Subtract $8$ from $- 2$ .

$- 20 m \leq - 10$

Step 3

Divide each term in $- 20 m \leq - 10$ by $- 20$ and simplify.

Divide each term in $- 20 m \leq - 10$ by $- 20$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 20 m}{- 20} \geq \frac{- 10}{- 20}$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 m}{- 20} \geq \frac{- 10}{- 20}$

Divide $m$ by $1$ .

$m \geq \frac{- 10}{- 20}$

Simplify the right side.

Cancel the common factor of $- 10$ and $- 20$ .

Factor $- 10$ out of $- 10$ .

$m \geq \frac{- 10 (1)}{- 20}$

Cancel the common factors.

Factor $- 10$ out of $- 20$ .

$m \geq \frac{- 10 \cdot 1}{- 10 \cdot 2}$

Cancel the common factor.

$m \geq \frac{- 10 \cdot 1}{- 10 \cdot 2}$

Rewrite the expression.

$m \geq \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$m \geq \frac{1}{2}$

Interval Notation:

$[\frac{1}{2}, \infty)$

Solve the Inequality for m -10m+8<=10m-2

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