Solve the inequality by yourselves and compare it to the incorrect solution.
Error: Split the inequality incorrectly. Correct Solution: -8≤ y ≤ -6
Practice makes perfect
In this exercise, we will find and correct the mistake in the solution of the given inequality. In order to determine the mistake, let's solve the inequality by ourselves. To solve an inequality of the form
| A|≤ b,
where A is a variable expression and b>0, we need to solve an "and" compound inequality. This is because we need the distance from the midpoint to be less than or equal to b units away.
- b< A< bIn our case, we can write our compound inequality as the following.
|y+7|≤ 1 ⇒ -1 ≤ y+7 ≤ 1
We can break this compound inequality into two separate cases.
Compound:& -1≤ y+7 ≤ 1
First Case: & -1≤ y+7
Second Case: & y+7 ≤ 1
In this step, we can already see the mistake in the given solution. The original solver's mistake was solving the compound inequality as if the inequality sign had been reversed.
| A| ≥ b *
Let's solve the inequalities one by one and find correct solution.
The solution set for the second case is all real numbers less than or equal to -6. Finally, we can combine these two solution sets to write a solution set for the compound inequality.
First Solution Set: & -8≤ y
Second Solution Set: & y ≤ -6
Compound Solution Set: & -8≤ y ≤ -6
