How do you solve 6(3a+1)-30=3(2a-4)?

2 Answers
May 8, 2018

a=1

Explanation:

Expand the terms first
18a+6-30=6a-12

Then shift the a terms to the left and the numbers to the right
18a-6a=-12-6+30
12a=12

Then divide both sides by 12
a=1

May 8, 2018

a = 1

Explanation:

6(3a+1)-30 = 3(2a-4)

First, to solve this, we use the distributive property, as shown here;
cdn.virtualnerd.comcdn.virtualnerd.com

Following this image, let's simplify color(blue)(6(3a+1)):
6 * 3a + 6 * 1 = 18a + 6

Now color(blue)(3(2a-4)):
3 * 2a + 3 * -4 = 6a - 12

Now let's put these back into the equation:
18a + 6 - 30 = 6a - 12

Combine color(blue)(6 - 30) = -24

18a - 24 = 6a - 12

Subtract color(blue)(6a) from both sides:
18a - 24 quadcolor(blue)(-quad6a) = 6a - 12 quadcolor(blue)(-quad6a)

12a - 24 = -12

Add color(blue)24 to both sides:
12a - 24 quadcolor(blue)(+quad24) = -12 quadcolor(blue)(+quad24)

12a = 12

Divide both sides by color(blue)(12):
(12a)/color(blue)12 = 12/color(blue)12

a = 1

Hope this helps!