Question

How do you solve and write the following in interval notation: `-2/5< -4/5x`?

Answer 1

See a solution process below:

Explanation:

Multiply each side of the inequality by `color(blue)((5/-4)` to solve for `x` 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)(5/-4) xx (-2)/5 color(red)(>) color(blue)(5/-4) xx (-4)/5x`

`(-10)/-20 color(red)(>) color(blue)(color(black)(cancel(color(blue)(5)))/color(black)(cancel(color(blue)(-4)))) xx color(blue)(cancel(color(black)(-4)))/color(blue)(cancel(color(black)(5)))x`

`1/2 > x`

Or, to state the inequality in terms of `x` we can reverse or "flip" the entire inequality:

`x < 1/2`

And, in interval notation:

`(-oo, 1/2)`