Question

How do you solve `-w/4<=-7` and graph the solution on a number line?

Answer 1

See a solution process below:

Explanation:

Multiply each side of the inequality by `color(blue)(-4)` to solve for `w` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

`color(blue)(-4) xx w/-4 color(red)(>=) color(blue)(-4) xx -7`

`cancel(color(blue)(-4)) xx w/color(blue)(cancel(color(black)(-4))) color(red)(>=) 28`

`w >= 28`

To graph this on the number line we draw a solid dot at `28` on the number line. The dot is solid because the inequality operator contains an "or equal to" clause. Therefore, 28 is part of the solution process.

Then we draw an arrow start at 28 and pointing to the right. It is pointing to the right because the inequality operator also contains a "greater than" clause: