Solve -3x-7-2(x-5)leq2(x-55)

$$- 3 x - 7 - 2 ( x - 5 ) \leq 2 ( x - 55 )$$

Solve for x

$$x\geq \frac{113}{7}$$

Solution Steps

Use the distributive property to multiply -2 by x-5.

$$-3x-7-2x+10\leq 2\left(x-55\right)$$

Combine -3x and -2x to get -5x.

$$-5x-7+10\leq 2\left(x-55\right)$$

Add -7 and 10 to get 3.

$$-5x+3\leq 2\left(x-55\right)$$

Use the distributive property to multiply 2 by x-55.

$$-5x+3\leq 2x-110$$

Subtract 2x from both sides.

$$-5x+3-2x\leq -110$$

Combine -5x and -2x to get -7x.

$$-7x+3\leq -110$$

Subtract 3 from both sides.

$$-7x\leq -110-3$$

Subtract 3 from -110 to get -113.

$$-7x\leq -113$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x\geq \frac{-113}{-7}$$

Fraction \frac{-113}{-7} can be simplified to \frac{113}{7} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{113}{7}$$