1. Solving Inequalities by Addition and Subtraction
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The phrase at least
can be expressed as ≥.
Example Variable: x
Inequality: 2x+4≥x+10
Solution Set: x≥6
To algebraically express a verbal inequality, we will need to translate the given information into mathematical symbols and operations.
at leastcan be expressed with the symbol ≥, which will be at the center of our expression.
is at least.If we let x represent
a number,we can form this expression.
is at least.
We can check our solution by substituting a few arbitrary values into the inequality translated above. The value satisfies the inequality if the inequality remains true after substituting and simplifying.
x | 2x+4≥10+x | Simplify |
---|---|---|
5 | 2(5)+4≥?10+5 | 14≱15 |
6 | 2(6)+4≥?10+6 | 16≥16 |
7 | 2(7)+4≥?10+7 | 18≥17 |
We can conclude that as long as x is greater than or equal to 6, the inequality is satisfied.