Solving inequalities is done in the same way as solving equations, using inverse operations to isolate the variable. Just remember to reverse the inequality symbol when multiplying or dividing the inequality by a negative number.
This tells us that all values less than - 2 satisfy the inequality. Knowing this, let's write the solution set.
{z|z<-2}
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.
z
5.6z+1.5 < 2.5z - 4.7
Evaluate
- 3
5.6( - 3)+1.5 < 2.5( - 3) - 4.7
- 15.3 < - 12.2
- 2
5.6( - 2)+1.5 < 2.5( - 2) - 4.7
- 9.7 ≮ - 9.7
-1
5.6( -1)+1.5 < 2.5( -1) - 4.7
-4.1 ≮ -7.2
We can conclude that, as long as z is less than - 2, the inequality is satisfied. This means our solution is correct.
