Question

Lin is solving the inequality 15-x< 14. She knows the solution to the equation 15 - x = 14 is x = 1 How can Lin determine whether x > Torx < 1 is the solution to the inequality?

Answer 1

The inequality we have is:

`15-x<14`

To solve this problem the x has to be positive, for this reason, the first step is to add x to both sides of the inequality:

`15-x+x<14+x`

As you can see, on the left side -x+x is equal to 0. So we have:

`15<14+x`

The next step to solving for x, now that the x is positive, is to leave the term with x alone on one side of the inequality. For this reason, we need to subtract 14 to both sides of the inequality:

`15-14<14-14+x`

On the right side, 14-14 is equal to 0, and thus we will be left only with "x" on that side:

And we can also write this solution with the x at the beginning:

[tex]x>1" src="
`image`

Answer: x>1