Solve 8(m-3)-5(3m+1)geq-2(2+4)

$$8 ( m - 3 ) - 5 ( 3 m + 1 ) \geq - 2 ( 2 + 4 )$$

Solve for m

$$m\leq -\frac{17}{7}$$

Solution Steps

Use the distributive property to multiply 8 by m-3.

$$8m-24-5\left(3m+1\right)\geq -2\left(2+4\right)$$

Use the distributive property to multiply -5 by 3m+1.

$$8m-24-15m-5\geq -2\left(2+4\right)$$

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

$$-7m-24-5\geq -2\left(2+4\right)$$

Subtract 5 from -24 to get -29.

$$-7m-29\geq -2\left(2+4\right)$$

Add 2 and 4 to get 6.

$$-7m-29\geq -2\times 6$$

Multiply -2 and 6 to get -12.

$$-7m-29\geq -12$$

Add 29 to both sides.

$$-7m\geq -12+29$$

Add -12 and 29 to get 17.

$$-7m\geq 17$$

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

$$m\leq -\frac{17}{7}$$