Solve for x -(55x)/2-10>=-185/2

$- \frac{55 x}{2} - 10 \geq - \frac{185}{2}$

Step 1

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

Add $10$ to both sides of the inequality.

$- \frac{55 x}{2} \geq - \frac{185}{2} + 10$

To write $10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{55 x}{2} \geq - \frac{185}{2} + 10 \cdot \frac{2}{2}$

Combine $10$ and $\frac{2}{2}$ .

$- \frac{55 x}{2} \geq - \frac{185}{2} + \frac{10 \cdot 2}{2}$

Combine the numerators over the common denominator.

$- \frac{55 x}{2} \geq \frac{- 185 + 10 \cdot 2}{2}$

Simplify the numerator.

Multiply $10$ by $2$ .

$- \frac{55 x}{2} \geq \frac{- 185 + 20}{2}$

Add $- 185$ and $20$ .

$- \frac{55 x}{2} \geq \frac{- 165}{2}$

Move the negative in front of the fraction.

$- \frac{55 x}{2} \geq - \frac{165}{2}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 55 x \geq - 165$

Step 3

Divide each term in $- 55 x \geq - 165$ by $- 55$ and simplify.

Divide each term in $- 55 x \geq - 165$ by $- 55$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 55 x}{- 55} \leq \frac{- 165}{- 55}$

Simplify the left side.

Cancel the common factor of $- 55$ .

Cancel the common factor.

$\frac{- 55 x}{- 55} \leq \frac{- 165}{- 55}$

Divide $x$ by $1$ .

$x \leq \frac{- 165}{- 55}$

Simplify the right side.

Divide $- 165$ by $- 55$ .

$x \leq 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 3$

Interval Notation:

$(- \infty, 3]$

Solve for x -(55x)/2-10>=-185/2

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