Solve a/2-5a-2/6geq1

$$\frac { a } { 2 } - \frac { 5 a - 2 } { 6 } \geq 1$$

Solve for a

$$a\leq -2$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,6. Since 6 is positive, the inequality direction remains the same.

$$3a-\left(5a-2\right)\geq 6$$

To find the opposite of 5a-2, find the opposite of each term.

$$3a-5a-\left(-2\right)\geq 6$$

The opposite of -2 is 2.

$$3a-5a+2\geq 6$$

Combine 3a and -5a to get -2a.

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

Subtract 2 from both sides.

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

Subtract 2 from 6 to get 4.

$$-2a\geq 4$$

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

$$a\leq \frac{4}{-2}$$

Divide 4 by -2 to get -2.

$$a\leq -2$$