Question

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

Answer 1

`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`

Answer 2

`a = 1`

Explanation:

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

First, to solve this, we use the distributive property, as shown here;

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!