Question

Please explain 12 and13and please please please hurry!

Answer 1

Answer:

12. a = 2

13. $x = \dfrac{4}{3}$

Step-by-step explanation:

12.

6a(a + 3) = 2a(3a + 5) + 16

First, distribute 6a on the left side, and distribute 2a on the right side.

6a² + 18a = 6a² + 10a + 16

Subtract 6a² from both sides.

18a = 10a + 16

Subtract 10a from both sides.

8a = 16

Divide both sides by 8.

a = 2

13.

$\dfrac{1}{3}x + \dfrac{1}{2}x = \dfrac{1}{3}(x + 2)$

The LCD of 2 and 3 is 6. We multiply both sides of the equation by 6 to get rid of all denominators.

$6 \times \dfrac{1}{3}x + 6 \times \dfrac{1}{2}x = 6 \times \dfrac{1}{3}(x + 2)$

$\dfrac{6}{3}x + \dfrac{6}{2}x = \dfrac{6}{3}(x + 2)$

$2x + 3x = 2(x + 2)$

Combine like terms on the left side. Distribute the 2 on the right side.

$5x = 2x + 4$

Subtract 2x from both sides.

$3x = 4$

Divide both sides by 3.

$x = \dfrac{4}{3}$