Solve for a 60a+64>=80a-92

$60 a + 64 \geq 80 a - 92$

Step 1

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

Subtract $80 a$ from both sides of the inequality.

$60 a + 64 - 80 a \geq - 92$

Subtract $80 a$ from $60 a$ .

$- 20 a + 64 \geq - 92$

Step 2

Move all terms not containing $a$ to the right side of the inequality.

Subtract $64$ from both sides of the inequality.

$- 20 a \geq - 92 - 64$

Subtract $64$ from $- 92$ .

$- 20 a \geq - 156$

Step 3

Divide each term in $- 20 a \geq - 156$ by $- 20$ and simplify.

Divide each term in $- 20 a \geq - 156$ by $- 20$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 20 a}{- 20} \leq \frac{- 156}{- 20}$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 a}{- 20} \leq \frac{- 156}{- 20}$

Divide $a$ by $1$ .

$a \leq \frac{- 156}{- 20}$

Simplify the right side.

Cancel the common factor of $- 156$ and $- 20$ .

Factor $- 4$ out of $- 156$ .

$a \leq \frac{- 4 (39)}{- 20}$

Cancel the common factors.

Factor $- 4$ out of $- 20$ .

$a \leq \frac{- 4 \cdot 39}{- 4 \cdot 5}$

Cancel the common factor.

$a \leq \frac{- 4 \cdot 39}{- 4 \cdot 5}$

Rewrite the expression.

$a \leq \frac{39}{5}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$a \leq \frac{39}{5}$

Interval Notation:

$(- \infty, \frac{39}{5}]$

Solve for a 60a+64>=80a-92

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