Solve the Inequality for x 6-8x+3<=-9x+7-x

$6 - 8 x + 3 \leq - 9 x + 7 - x$

Rewrite so $x$ is on the left side of the inequality.

$- 9 x + 7 - x \geq 6 - 8 x + 3$

Subtract $x$ from $- 9 x$ .

$- 10 x + 7 \geq 6 - 8 x + 3$

Add $6$ and $3$ .

$- 10 x + 7 \geq - 8 x + 9$

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

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

$- 10 x + 7 + 8 x \geq 9$

Add $- 10 x$ and $8 x$ .

$- 2 x + 7 \geq 9$

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

Subtract $7$ from both sides of the inequality.

$- 2 x \geq 9 - 7$

Subtract $7$ from $9$ .

$- 2 x \geq 2$

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

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

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

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 $- 2$ .

$x \leq - 1$

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 1$

Interval Notation:

$(- \infty, - 1]$

Solve the Inequality for x 6-8x+3<=-9x+7-x

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