Solve a-8/4>a-12+10/6

$$\frac { a - 8 } { 4 } > \frac { a - 12 + 10 } { 6 }$$

Solve for a

$$a>20$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,6. Since 12 is positive, the inequality direction remains the same.

$$3\left(a-8\right)>2\left(a-12+10\right)$$

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

$$3a-24>2\left(a-12+10\right)$$

Add -12 and 10 to get -2.

$$3a-24>2\left(a-2\right)$$

Use the distributive property to multiply 2 by a-2.

$$3a-24>2a-4$$

Subtract 2a from both sides.

$$3a-24-2a>-4$$

Combine 3a and -2a to get a.

$$a-24>-4$$

Add 24 to both sides.

$$a>-4+24$$

Add -4 and 24 to get 20.

$$a>20$$