Solve a-4/3geq2a+2/4

$$\frac { a - 4 } { 3 } \geq \frac { 2 a + 2 } { 4 }$$

Solve for a

$$a\leq -11$$

Solution Steps

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

$$4\left(a-4\right)\geq 3\left(2a+2\right)$$

Use the distributive property to multiply 4 by a-4.

$$4a-16\geq 3\left(2a+2\right)$$

Use the distributive property to multiply 3 by 2a+2.

$$4a-16\geq 6a+6$$

Subtract 6a from both sides.

$$4a-16-6a\geq 6$$

Combine 4a and -6a to get -2a.

$$-2a-16\geq 6$$

Add 16 to both sides.

$$-2a\geq 6+16$$

Add 6 and 16 to get 22.

$$-2a\geq 22$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$a\leq \frac{22}{-2}$$

Divide 22 by -2 to get -11.

$$a\leq -11$$