Solve for x -4x+10>=5x+55

$- 4 x + 10 \geq 5 x + 55$

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

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

$- 4 x + 10 - 5 x \geq 55$

Subtract $5 x$ from $- 4 x$ .

$- 9 x + 10 \geq 55$

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

Subtract $10$ from both sides of the inequality.

$- 9 x \geq 55 - 10$

Subtract $10$ from $55$ .

$- 9 x \geq 45$

Divide each term in $- 9 x \geq 45$ by $- 9$ and simplify.

Divide each term in $- 9 x \geq 45$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 x}{- 9} \leq \frac{45}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} \leq \frac{45}{- 9}$

Divide $x$ by $1$ .

$x \leq \frac{45}{- 9}$

Simplify the right side.

Divide $45$ by $- 9$ .

$x \leq - 5$

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 5$

Interval Notation:

$(- \infty, - 5]$

Solve for x -4x+10>=5x+55

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