Question

How do you solve `4(x – 3) + 4 <10 + 6x`?

Answer 1

`x>9`

Explanation:

Expand the bracket on the LHS by multiplying `x` with `4` and `-3` with `4`.

`4x-12+4<10+6x`

`4x-8<10+6x`

`4x<18+6x`

`-2x<18`

Now, divide the entire equation by `-2`. But keep in mind the the equality sign FLIPS when you divide by a negative number.

`x>9`

Below is the graph of this inequalities.

graph{x>9 [-0.76, 72.3, 0.74, 37.27]}

Answer 2

See a solution process below:

Explanation:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

`color(red)(4)(x - 3) + 4 < 10 + 6x`

`(color(red)(4) * x) - (color(red)(4) * 3) + 4 < 10 + 6x`

`4x - 12 + 4 < 10 + 6x`

`4x - 8 < 10 + 6x`

Next, subtract `color(red)(4x)` and `color(blue)(10)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`4x - 8 - color(red)(4x) - color(blue)(10) < 10 + 6x - color(red)(4x) - color(blue)(10)`

`4x - color(red)(4x) - 8 - color(blue)(10) < 10 - color(blue)(10) + 6x - color(red)(4x)`

`0 - 18 < 0 + (6 - color(red)(4))x`

`-18 < 2x`

Now, divide each side of the inequality by `color(red)(2)` to solve for `x` while keeping the equation balanced:

`-18/color(red)(2) < (2x)/color(red)(2)`

`-9 < (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2))`

`-9 < x`

To state the solution in terms of `x` we can reverse or "flip" the entire inequality:

`x > -9`