Question

How do you solve `-32- 7a > - 4( 1+ a ) - 7a`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms in parenthesis on the right side of the inequality by multiplying the terms within the parenthesis by the term outside the parenthesis:

`-32 - 7a > color(red)(-4)(1 + a) - 7a`

`-32 - 7a > (color(red)(-4) xx 1) + (color(red)(-4) xx a) - 7a`

`-32 - 7a > -4 - 4a - 7a`

Next, combine like terms on the right side of the inequality:

`-32 - 7a > -4 + (-4 - 7)a`

`-32 - 7a > -4 + (-11)a`

`-32 - 7a > -4 - 11a`

Then, add `color(red)(11a)` and `color(blue)(32)` to each side of the inequality to isolate the `a` term while keeping the inequality balanced:

`color(blue)(32) - 32 - 7a + color(red)(11a) > color(blue)(32) - 4 - 11a + color(red)(11a)`

`0 + (-7 + color(red)(11))a > 28 - 0`

`4a > 28`

Now, divide each side of the inequality by `color(red)(4)` to solve for `a` while keeping the inequality balanced:

`(4a)/color(red)(4) > 28/color(red)(4)`

`(color(red)(cancel(color(black)(4)))a)/cancel(color(red)(4)) > 7`

`a > 7`