To algebraically express a verbal inequality, we will need to translate the given information into mathematical symbols and operations.
Writing the Inequality
The phrase is more than can be expressed as >. This symbol will be at the center of our expression.
... >...
We will translate any verbal expression that comes beforeis more than on the left-hand side of the inequality symbol. If we let n represent a number, we can form this expression.
twice a number
2 n
On the right-hand side of the inequality symbol we will translate any verbal expression that comes afteris more than.
the sum of that number and 9
n + 9
Finally, we can bring these two expressions together to form the inequality.
2n>n+9
This solution tells us that all values greater than 9 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.
n
2n>n+9
Simplify
8
2( 8)? > 8+9
16≯ 17
9
2( 9)? > 9+9
18≯ 18
10
2( 10)? > 10+9
20>19
We can conclude that as long as n is greater than 9, the inequality is satisfied.
