Solve the Inequality for x -5(3x-6)+5>=-25

$- 5 (3 x - 6) + 5 \geq - 25$

Step 1

Simplify $- 5 (3 x - 6) + 5$ .

Simplify each term.

Apply the distributive property.

$- 5 (3 x) - 5 \cdot - 6 + 5 \geq - 25$

Multiply $3$ by $- 5$ .

$- 15 x - 5 \cdot - 6 + 5 \geq - 25$

Multiply $- 5$ by $- 6$ .

$- 15 x + 30 + 5 \geq - 25$

Add $30$ and $5$ .

$- 15 x + 35 \geq - 25$

Step 2

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

Subtract $35$ from both sides of the inequality.

$- 15 x \geq - 25 - 35$

Subtract $35$ from $- 25$ .

$- 15 x \geq - 60$

Step 3

Divide each term in $- 15 x \geq - 60$ by $- 15$ and simplify.

Divide each term in $- 15 x \geq - 60$ by $- 15$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 15 x}{- 15} \leq \frac{- 60}{- 15}$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 x}{- 15} \leq \frac{- 60}{- 15}$

Divide $x$ by $1$ .

$x \leq \frac{- 60}{- 15}$

Simplify the right side.

Divide $- 60$ by $- 15$ .

$x \leq 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 4$

Interval Notation:

$(- \infty, 4]$

Solve the Inequality for x -5(3x-6)+5>=-25

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