Solve a-1/4-1>a+1/3+8

$$\frac { a - 1 } { 4 } - 1 > \frac { a + 1 } { 3 } + 8$$

Solve for a

$$a<-115$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3. Since 12 is positive, the inequality direction remains the same.

$$3\left(a-1\right)-12>4\left(a+1\right)+96$$

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

$$3a-3-12>4\left(a+1\right)+96$$

Subtract 12 from -3 to get -15.

$$3a-15>4\left(a+1\right)+96$$

Use the distributive property to multiply 4 by a+1.

$$3a-15>4a+4+96$$

Add 4 and 96 to get 100.

$$3a-15>4a+100$$

Subtract 4a from both sides.

$$3a-15-4a>100$$

Combine 3a and -4a to get -a.

$$-a-15>100$$

Add 15 to both sides.

$$-a>100+15$$

Add 100 and 15 to get 115.

$$-a>115$$

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

$$a<-115$$