Solve 4*(2m-5)geq3*(5m-3)-32

$$4 \cdot ( 2 m - 5 ) \geq 3 \cdot ( 5 m - 3 ) - 32$$

Solve for m

$$m\leq 3$$

Solution Steps

Use the distributive property to multiply 4 by 2m-5.

$$8m-20\geq 3\left(5m-3\right)-32$$

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

$$8m-20\geq 15m-9-32$$

Subtract 32 from -9 to get -41.

$$8m-20\geq 15m-41$$

Subtract 15m from both sides.

$$8m-20-15m\geq -41$$

Combine 8m and -15m to get -7m.

$$-7m-20\geq -41$$

Add 20 to both sides.

$$-7m\geq -41+20$$

Add -41 and 20 to get -21.

$$-7m\geq -21$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$m\leq \frac{-21}{-7}$$

Divide -21 by -7 to get 3.

$$m\leq 3$$