Solve 2(2x-5)leq3(3x+1)-4

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

Solve for x

$$x\geq -\frac{9}{5}$$

Solution Steps

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

$$4x-10\leq 3\left(3x+1\right)-4$$

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

$$4x-10\leq 9x+3-4$$

Subtract 4 from 3 to get -1.

$$4x-10\leq 9x-1$$

Subtract 9x from both sides.

$$4x-10-9x\leq -1$$

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

$$-5x-10\leq -1$$

Add 10 to both sides.

$$-5x\leq -1+10$$

Add -1 and 10 to get 9.

$$-5x\leq 9$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\geq -\frac{9}{5}$$