Question

How do you solve `-8( x + 3.5) \leq - 3( 4.2+ x )`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms on each side of the inequality by multiplying the terms within the parenthesis by the terms outside the parenthesis:

`color(red)(-8)(x + 3.5) <= color(blue)(-3)(4.2 + x)`

`(color(red)(-8) xx x) + (color(red)(-8) xx 3.5) <= (color(blue)(-3) xx 4.2) + (color(blue)(-3) xx x)`

`-8x + (-28) <= -12.6 + (-3x)`

`-8x - 28 <= -12.6 - 3x`

Next, add `color(red)(8x)` and `color(blue)(12.6)` to each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`-8x - 28 + color(red)(8x) + color(blue)(12.6) <= -12.6 - 3x + color(red)(8x) + color(blue)(12.6)`

`-8x + color(red)(8x) - 28 + color(blue)(12.6) <= -12.6 + color(blue)(12.6) - 3x + color(red)(8x)`

`0 - 15.4 <= 0 + (-3 + color(red)(8))x`

`-15.4 <= 5x`

Now, divide each side of the inequality by `color(red)(5)` to solve for `x` while keeping the inequality balanced:

`-15.4/color(red)(5) <= (5x)/color(red)(5)`

`-3.08 <= (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5))`

`-3.08 <= x`

We can state the solution in terms of `x` by reversing or "flipping" the entire inequality:

`x >= -3.08`