Solve 9/2-1leq2a/3+2

$$\frac { 9 } { 2 } - 1 \leq \frac { 2 a } { 3 } + 2$$

Solve for a

$$a\geq \frac{9}{4}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.

$$27-6\leq 2\times 2a+12$$

Subtract 6 from 27 to get 21.

$$21\leq 2\times 2a+12$$

Multiply 2 and 2 to get 4.

$$21\leq 4a+12$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$4a+12\geq 21$$

Subtract 12 from both sides.

$$4a\geq 21-12$$

Subtract 12 from 21 to get 9.

$$4a\geq 9$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$a\geq \frac{9}{4}$$