Solve for a a/2-3>=2a

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

Step 1

Move all terms containing $a$ to the left side of the inequality.

Subtract $2 a$ from both sides of the inequality.

$\frac{a}{2} - 3 - 2 a \geq 0$

To write $- 2 a$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{a}{2} - 2 a \cdot \frac{2}{2} - 3 \geq 0$

Combine $- 2 a$ and $\frac{2}{2}$ .

$\frac{a}{2} + \frac{- 2 a \cdot 2}{2} - 3 \geq 0$

Combine the numerators over the common denominator.

$\frac{a - 2 a \cdot 2}{2} - 3 \geq 0$

Simplify each term.

Simplify the numerator.

Factor $a$ out of $a - 2 a \cdot 2$ .

Raise $a$ to the power of $1$ .

$\frac{a^{1} - 2 a \cdot 2}{2} - 3 \geq 0$

Factor $a$ out of $a^{1}$ .

$\frac{a \cdot 1 - 2 a \cdot 2}{2} - 3 \geq 0$

Factor $a$ out of $- 2 a \cdot 2$ .

$\frac{a \cdot 1 + a (- 2 \cdot 2)}{2} - 3 \geq 0$

Factor $a$ out of $a \cdot 1 + a (- 2 \cdot 2)$ .

$\frac{a (1 - 2 \cdot 2)}{2} - 3 \geq 0$

Multiply $- 2$ by $2$ .

$\frac{a (1 - 4)}{2} - 3 \geq 0$

Subtract $4$ from $1$ .

$\frac{a \cdot - 3}{2} - 3 \geq 0$

Move $- 3$ to the left of $a$ .

$\frac{- 3 \cdot a}{2} - 3 \geq 0$

Move the negative in front of the fraction.

$- \frac{3 a}{2} - 3 \geq 0$

Step 2

Add $3$ to both sides of the inequality.

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

Step 3

Divide each term in $- \frac{3 a}{2} \geq 3$ by $- 1$ and simplify.

Divide each term in $- \frac{3 a}{2} \geq 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $\frac{3 a}{2}$ by $1$ .

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

Simplify the right side.

Divide $3$ by $- 1$ .

$\frac{3 a}{2} \leq - 3$

Step 4

Multiply both sides by $2$ .

$\frac{3 a}{2} \cdot 2 \leq - 3 \cdot 2$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 a}{2} \cdot 2 \leq - 3 \cdot 2$

Rewrite the expression.

$3 a \leq - 3 \cdot 2$

Simplify the right side.

Multiply $- 3$ by $2$ .

$3 a \leq - 6$

Step 6

Divide each term in $3 a \leq - 6$ by $3$ and simplify.

Divide each term in $3 a \leq - 6$ by $3$ .

$\frac{3 a}{3} \leq \frac{- 6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 a}{3} \leq \frac{- 6}{3}$

Divide $a$ by $1$ .

$a \leq \frac{- 6}{3}$

Simplify the right side.

Divide $- 6$ by $3$ .

$a \leq - 2$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$a \leq - 2$

Interval Notation:

$(- \infty, - 2]$

Solve for a a/2-3>=2a

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