Example Variable: x Inequality: 2x+4≥ x+10 Solution Set: x≥ 6
Practice makes perfect
To algebraically express a verbal inequality, we will need to translate the given information into mathematical symbols and operations.
Writing the Inequality
The phrase at least can be expressed with the symbol ≥, which will be at the center of our expression.
... ≥...
On the left-hand side of the inequality symbol, we will translate any verbal expression that comes before the phrase is at least. If we let x represent a number, we can form this expression.
twice a number increased by4
2 x + 4
On the right-hand side of the inequality symbol, we will translate any verbal expression that comes afteris at least.
10more than the number
x + 10
Finally, we can bring these two expressions together to form the inequality.
2x+4≥ x+10
This solution tells us that all values greater than or equal to 6 will satisfy the inequality.
Checking Our Solution
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.
