Solve 5x-2(3x-4)leq4[2x-3(1-3x)]

$$5 x - 2 ( 3 x - 4 ) \leq 4 [ 2 x - 3 ( 1 - 3 x ) ]$$

Solve for x

$$x\geq \frac{4}{9}$$

Solution Steps

Use the distributive property to multiply -2 by 3x-4.

$$5x-6x+8\leq 4\left(2x-3\left(1-3x\right)\right)$$

Combine 5x and -6x to get -x.

$$-x+8\leq 4\left(2x-3\left(1-3x\right)\right)$$

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

$$-x+8\leq 4\left(2x-3+9x\right)$$

Combine 2x and 9x to get 11x.

$$-x+8\leq 4\left(11x-3\right)$$

Use the distributive property to multiply 4 by 11x-3.

$$-x+8\leq 44x-12$$

Subtract 44x from both sides.

$$-x+8-44x\leq -12$$

Combine -x and -44x to get -45x.

$$-45x+8\leq -12$$

Subtract 8 from both sides.

$$-45x\leq -12-8$$

Subtract 8 from -12 to get -20.

$$-45x\leq -20$$

Divide both sides by -45. Since -45 is negative, the inequality direction is changed.

$$x\geq \frac{-20}{-45}$$

Reduce the fraction \frac{-20}{-45} to lowest terms by extracting and canceling out -5.

$$x\geq \frac{4}{9}$$