Question

How do you solve and write the following in interval notation: `2x < 10` and `-5x < 5`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve the first inequality as:

`2x < 10`

`(2x)/color(red)(2) < 10/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 5`

`x < 5`

Step 2) Solve the second equality. Remember, when multiplying or dividing an inequality by a negative number you must reverse the inequality operator:

`-5x < 5`

`(-5x)/color(red)(-5) color(red)(>) 5/color(red)(-5)`

`(color(red)(cancel(color(black)(-5)))x)/cancel(color(red)(-5)) color(red)(>) -1`

`x > -1`

Step 3) Combine the solutions and write the solution in interval notation:

`x > -1` and `x < 5`

`(-1, 5)`