Solve the Inequality for x -8x-10<-6x+2<=-8x+4

$- 8 x - 10 < - 6 x + 2 \leq - 8 x + 4$

Solve $- 8 x - 10 < - 6 x + 2$ for $x$ .

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

Add $6 x$ to both sides of the inequality.

$- 8 x - 10 + 6 x < 2$

Add $- 8 x$ and $6 x$ .

$- 2 x - 10 < 2$

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

Add $10$ to both sides of the inequality.

$- 2 x < 2 + 10$

Add $2$ and $10$ .

$- 2 x < 12$

Divide each term in $- 2 x < 12$ by $- 2$ and simplify.

Divide each term in $- 2 x < 12$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} > \frac{12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} > \frac{12}{- 2}$

Divide $x$ by $1$ .

$x > \frac{12}{- 2}$

Simplify the right side.

Divide $12$ by $- 2$ .

$x > - 6$

Solve $- 6 x + 2 \leq - 8 x + 4$ for $x$ .

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

Add $8 x$ to both sides of the inequality.

$- 6 x + 2 + 8 x \leq 4$

Add $- 6 x$ and $8 x$ .

$2 x + 2 \leq 4$

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

Subtract $2$ from both sides of the inequality.

$2 x \leq 4 - 2$

Subtract $2$ from $4$ .

$2 x \leq 2$

Divide each term in $2 x \leq 2$ by $2$ and simplify.

Divide each term in $2 x \leq 2$ by $2$ .

$\frac{2 x}{2} \leq \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{2}{2}$

Divide $x$ by $1$ .

$x \leq \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

$x \leq 1$

Find the intersection of $x > - 6$ and $x \leq 1$ .

$- 6 < x \leq 1$

The result can be shown in multiple forms.

Inequality Form:

$- 6 < x \leq 1$

Interval Notation:

$(- 6, 1]$

Solve the Inequality for x -8x-10<-6x+2<=-8x+4

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