Solve 5x-3(3x-3+2x)geq2(3x-20+4x)

$$5 x - 3 ( 3 x - 3 + 2 x ) \geq 2 ( 3 x - 20 + 4 x )$$

Solve for x

$$x\leq \frac{49}{24}$$

Solution Steps

Combine 3x and 2x to get 5x.

$$5x-3\left(5x-3\right)\geq 2\left(3x-20+4x\right)$$

Use the distributive property to multiply -3 by 5x-3.

$$5x-15x+9\geq 2\left(3x-20+4x\right)$$

Combine 5x and -15x to get -10x.

$$-10x+9\geq 2\left(3x-20+4x\right)$$

Combine 3x and 4x to get 7x.

$$-10x+9\geq 2\left(7x-20\right)$$

Use the distributive property to multiply 2 by 7x-20.

$$-10x+9\geq 14x-40$$

Subtract 14x from both sides.

$$-10x+9-14x\geq -40$$

Combine -10x and -14x to get -24x.

$$-24x+9\geq -40$$

Subtract 9 from both sides.

$$-24x\geq -40-9$$

Subtract 9 from -40 to get -49.

$$-24x\geq -49$$

Divide both sides by -24. Since -24 is negative, the inequality direction is changed.

$$x\leq \frac{-49}{-24}$$

Fraction \frac{-49}{-24} can be simplified to \frac{49}{24} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{49}{24}$$