Solve 7-4(5x-3)leq2(3-x)-5

$$7-4(5x-3) \leq 2(3-x)-5$$

Solve for x

$$x\geq 1$$

Solution Steps

Use the distributive property to multiply -4 by 5x-3.

$$7-20x+12\leq 2\left(3-x\right)-5$$

Add 7 and 12 to get 19.

$$19-20x\leq 2\left(3-x\right)-5$$

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

$$19-20x\leq 6-2x-5$$

Subtract 5 from 6 to get 1.

$$19-20x\leq 1-2x$$

Add 2x to both sides.

$$19-20x+2x\leq 1$$

Combine -20x and 2x to get -18x.

$$19-18x\leq 1$$

Subtract 19 from both sides.

$$-18x\leq 1-19$$

Subtract 19 from 1 to get -18.

$$-18x\leq -18$$

Divide both sides by -18. Since -18 is negative, the inequality direction is changed.

$$x\geq \frac{-18}{-18}$$

Divide -18 by -18 to get 1.

$$x\geq 1$$