Solve (6x-3)-(8x-5)geq-(3x+9)+(2x-4)

$$( 6 x - 3 ) - ( 8 x - 5 ) \geq - ( 3 x + 9 ) + ( 2 x - 4 )$$

Solve for x

$$x\leq 15$$

Solution Steps

To find the opposite of 8x-5, find the opposite of each term.

$$6x-3-8x-\left(-5\right)\geq -\left(3x+9\right)+2x-4$$

The opposite of -5 is 5.

$$6x-3-8x+5\geq -\left(3x+9\right)+2x-4$$

Combine 6x and -8x to get -2x.

$$-2x-3+5\geq -\left(3x+9\right)+2x-4$$

Add -3 and 5 to get 2.

$$-2x+2\geq -\left(3x+9\right)+2x-4$$

To find the opposite of 3x+9, find the opposite of each term.

$$-2x+2\geq -3x-9+2x-4$$

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

$$-2x+2\geq -x-9-4$$

Subtract 4 from -9 to get -13.

$$-2x+2\geq -x-13$$

Add x to both sides.

$$-2x+2+x\geq -13$$

Combine -2x and x to get -x.

$$-x+2\geq -13$$

Subtract 2 from both sides.

$$-x\geq -13-2$$

Subtract 2 from -13 to get -15.

$$-x\geq -15$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\leq \frac{-15}{-1}$$

Fraction \frac{-15}{-1} can be simplified to 15 by removing the negative sign from both the numerator and the denominator.

$$x\leq 15$$