Solve the Inequality for a 8a+2(1-5a)<=20

$8 a + 2 (1 - 5 a) \leq 20$

Step 1

Simplify $8 a + 2 (1 - 5 a)$ .

Simplify each term.

Apply the distributive property.

$8 a + 2 \cdot 1 + 2 (- 5 a) \leq 20$

Multiply $2$ by $1$ .

$8 a + 2 + 2 (- 5 a) \leq 20$

Multiply $- 5$ by $2$ .

$8 a + 2 - 10 a \leq 20$

Subtract $10 a$ from $8 a$ .

$- 2 a + 2 \leq 20$

Step 2

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

Subtract $2$ from both sides of the inequality.

$- 2 a \leq 20 - 2$

Subtract $2$ from $20$ .

$- 2 a \leq 18$

Step 3

Divide each term in $- 2 a \leq 18$ by $- 2$ and simplify.

Divide each term in $- 2 a \leq 18$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 a}{- 2} \geq \frac{18}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 a}{- 2} \geq \frac{18}{- 2}$

Divide $a$ by $1$ .

$a \geq \frac{18}{- 2}$

Simplify the right side.

Divide $18$ by $- 2$ .

$a \geq - 9$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$a \geq - 9$

Interval Notation:

$[- 9, \infty)$

Solve the Inequality for a 8a+2(1-5a)<=20

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