Solve for a 3a+1>(-7a-14)/-4

$3 a + 1 > \frac{- 7 a - 14}{- 4}$

Step 1

Multiply both sides by $- 4$ .

$(3 a + 1) \cdot - 4 < \frac{- 7 a - 14}{- 4} \cdot - 4$

Step 2

Simplify.

Simplify the left side.

Simplify $(3 a + 1) \cdot - 4$ .

Apply the distributive property.

$3 a \cdot - 4 + 1 \cdot - 4 < \frac{- 7 a - 14}{- 4} \cdot - 4$

Multiply.

Multiply $- 4$ by $3$ .

$- 12 a + 1 \cdot - 4 < \frac{- 7 a - 14}{- 4} \cdot - 4$

Multiply $- 4$ by $1$ .

$- 12 a - 4 < \frac{- 7 a - 14}{- 4} \cdot - 4$

Simplify the right side.

Simplify $\frac{- 7 a - 14}{- 4} \cdot - 4$ .

Factor $7$ out of $- 7 a - 14$ .

Factor $7$ out of $- 7 a$ .

$- 12 a - 4 < \frac{7 (- a) - 14}{- 4} \cdot - 4$

Factor $7$ out of $- 14$ .

$- 12 a - 4 < \frac{7 (- a) + 7 (- 2)}{- 4} \cdot - 4$

Factor $7$ out of $7 (- a) + 7 (- 2)$ .

$- 12 a - 4 < \frac{7 (- a - 2)}{- 4} \cdot - 4$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

$- 12 a - 4 < \frac{7 (- a - 2)}{4 (- 1)} \cdot - 4$

Factor $4$ out of $- 4$ .

$- 12 a - 4 < \frac{7 (- a - 2)}{4 \cdot - 1} \cdot (4 \cdot - 1)$

Cancel the common factor.

$- 12 a - 4 < \frac{7 (- a - 2)}{4 \cdot - 1} \cdot (4 \cdot - 1)$

Rewrite the expression.

$- 12 a - 4 < \frac{7 (- a - 2)}{- 1} \cdot - 1$

Combine $\frac{7 (- a - 2)}{- 1}$ and $- 1$ .

$- 12 a - 4 < \frac{7 (- a - 2) \cdot - 1}{- 1}$

Simplify the expression.

Multiply $- 1$ by $7$ .

$- 12 a - 4 < \frac{- 7 (- a - 2)}{- 1}$

Move the negative one from the denominator of $\frac{- 7 (- a - 2)}{- 1}$ .

$- 12 a - 4 < - 1 \cdot (- 7 (- a - 2))$

Rewrite $- 1 \cdot (- 7 (- a - 2))$ as $- (- 7 (- a - 2))$ .

$- 12 a - 4 < - (- 7 (- a - 2))$

Apply the distributive property.

$- 12 a - 4 < - (- 7 (- a) - 7 \cdot - 2)$

Multiply.

Multiply $- 1$ by $- 7$ .

$- 12 a - 4 < - (7 a - 7 \cdot - 2)$

Multiply $- 7$ by $- 2$ .

$- 12 a - 4 < - (7 a + 14)$

Apply the distributive property.

$- 12 a - 4 < - (7 a) - 1 \cdot 14$

Multiply.

Multiply $7$ by $- 1$ .

$- 12 a - 4 < - 7 a - 1 \cdot 14$

Multiply $- 1$ by $14$ .

$- 12 a - 4 < - 7 a - 14$

Step 3

Solve for $a$ .

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

Add $7 a$ to both sides of the inequality.

$- 12 a - 4 + 7 a < - 14$

Add $- 12 a$ and $7 a$ .

$- 5 a - 4 < - 14$

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

Add $4$ to both sides of the inequality.

$- 5 a < - 14 + 4$

Add $- 14$ and $4$ .

$- 5 a < - 10$

Divide each term in $- 5 a < - 10$ by $- 5$ and simplify.

Divide each term in $- 5 a < - 10$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 a}{- 5} > \frac{- 10}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 a}{- 5} > \frac{- 10}{- 5}$

Divide $a$ by $1$ .

$a > \frac{- 10}{- 5}$

Simplify the right side.

Divide $- 10$ by $- 5$ .

$a > 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$a > 2$

Interval Notation:

$(2, \infty)$

Solve for a 3a+1>(-7a-14)/-4

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