Question

How do you solve `-7(1-4x)+8(1-6x)<=41`?

Answer 1

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)(-7)(1 - 4x) + color(blue)(8)(1 - 6x) <= 41`

`(color(red)(-7) xx 1) + (color(red)(-7) xx -4x) + (color(blue)(8) xx 1) - (color(blue)(8) xx 6x) <= 41`

`-7 + 28x + 8 - 48x <= 41`

Next, group and combine like terms on the left side of the inequality:

`-7 + 8 + 28x - 48x <= 41`

`(-7 + 8) + (28 - 48)x <= 41`

`1 + (-20)x <= 41`

`1 - 20x <= 41`

Then, subtract `color(red)(1)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced::

`-color(red)(1) + 1 - 20x <= -color(red)(1) + 41`

`0 - 20x <= 40`

`-20x <= 40`

Now, divide each side of the inequality by `color(blue)(-20)` to solve for `x` while keeping the inequality balanced. However, because we are multiplying or dividing and inequality by a negative number we must reverse the inequality operator:

`(-20x)/color(blue)(-20) color(red)(>=) 40/color(blue)(-20)`

`(color(red)(cancel(color(black)(-20)))x)/cancel(color(blue)(-20)) color(red)(>=) -2`#

`x >= -2`