Solve 2a-9>3(a-1)-8

$$2 a - 9 > 3 ( a - 1 ) - 8$$

Solve for a

$$a<2$$

Solution Steps

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

$$2a-9>3a-3-8$$

Subtract 8 from -3 to get -11.

$$2a-9>3a-11$$

Subtract 3a from both sides.

$$2a-9-3a>-11$$

Combine 2a and -3a to get -a.

$$-a-9>-11$$

Add 9 to both sides.

$$-a>-11+9$$

Add -11 and 9 to get -2.

$$-a>-2$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$a<\frac{-2}{-1}$$

Fraction \frac{-2}{-1} can be simplified to 2 by removing the negative sign from both the numerator and the denominator.

$$a<2$$