Answer:
12. a = 2
13. [tex] x = \dfrac{4}{3} [/tex]
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.
[tex] \dfrac{1}{3}x + \dfrac{1}{2}x = \dfrac{1}{3}(x + 2) [/tex]
The LCD of 2 and 3 is 6. We multiply both sides of the equation by 6 to get rid of all denominators.
[tex] 6 \times \dfrac{1}{3}x + 6 \times \dfrac{1}{2}x = 6 \times \dfrac{1}{3}(x + 2) [/tex]
[tex] \dfrac{6}{3}x + \dfrac{6}{2}x = \dfrac{6}{3}(x + 2) [/tex]
[tex] 2x + 3x = 2(x + 2) [/tex]
Combine like terms on the left side. Distribute the 2 on the right side.
[tex] 5x = 2x + 4 [/tex]
Subtract 2x from both sides.
[tex] 3x = 4 [/tex]
Divide both sides by 3.
[tex] x = \dfrac{4}{3} [/tex]
