Solve 5x+9(2-x)>3(x+1)-4(2+x)-3

$$5x+9(2-x) > 3(x+1)-4(2+x)-3$$

Solve for x

$$x<\frac{26}{3}$$

Solution Steps

Use the distributive property to multiply 9 by 2-x.

$$5x+18-9x>3\left(x+1\right)-4\left(2+x\right)-3$$

Combine 5x and -9x to get -4x.

$$-4x+18>3\left(x+1\right)-4\left(2+x\right)-3$$

Use the distributive property to multiply 3 by x+1.

$$-4x+18>3x+3-4\left(2+x\right)-3$$

Use the distributive property to multiply -4 by 2+x.

$$-4x+18>3x+3-8-4x-3$$

Subtract 8 from 3 to get -5.

$$-4x+18>3x-5-4x-3$$

Combine 3x and -4x to get -x.

$$-4x+18>-x-5-3$$

Subtract 3 from -5 to get -8.

$$-4x+18>-x-8$$

Add x to both sides.

$$-4x+18+x>-8$$

Combine -4x and x to get -3x.

$$-3x+18>-8$$

Subtract 18 from both sides.

$$-3x>-8-18$$

Subtract 18 from -8 to get -26.

$$-3x>-26$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x<\frac{-26}{-3}$$

Fraction \frac{-26}{-3} can be simplified to \frac{26}{3} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{26}{3}$$