Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when you divide or multiply by a negative number, you must reverse the inequality sign.
This tells us that all values less than 14 satisfy the inequality. Knowing this, let's write the solution set.
{h|h<14}
Graphing Our Solution
Below we demonstrate the inequality by graphing the solution set on a number line. Notice that since the inequality is strict, h cannot equal 14. We show this with an open circle on the number line.
Checking Our Solution
We can check our solution by substituting a few arbitrary values into the given inequality. The value satisfies the inequality if the inequality remains true after substituting and simplifying.
h
6-h>-8
Evaluate
13
6- 13>-8
- 7> - 8
14
6- 14>-8
- 8 ≯ - 8
15
6- 15>-8
-9 ≯ - 8
We can conclude that, as long as h is less than 14, the inequality is satisfied. This means our solution is correct.
