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.
Solving the Inequality
Before we can solve for m, we need to combine the m-terms on one side of the inequality. To do that, we will start by distributing to eliminate the parentheses.
This tells us that all values greater than or equal to 18 satisfy the inequality. Knowing this, let's write the solution set.
{m|m≥18}
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.
m
0.7(2m-5) ≥ 21.7
Evaluate
17
0.7(2( 17)-5) ≥ 21.7
20.3 ≱ 21.7
18
0.7(2( 18)-5) ≥ 21.7
21.7 ≥ 21.7
19
0.7(2( 19)-5) ≥ 21.7
23.1 ≥ 21.7
We can conclude that, as long as m is greater than or equal to 18, the inequality is satisfied. This means our solution is correct.
