Variable: Let x represent the number. Inequality: - 3x+4<5x+8 Solution set: {x| x>- 12}
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 is less than can be expressed as <. This symbol 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 beforeis less than. If we let x represent a number, we can form an expression.
Negative three times a number plus4
-3 x +4
On the right-hand side of the inequality symbol, we will translate any verbal expression that comes afteris less than.
five times the number plus8
5 x +8
Finally, we can bring these two expressions together to form the inequality.
-3x+4< 5x+8
Now, we can write the solution set.
{x|x>-1/2}
This solution tells us that all values greater than - 12 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
- 3x+4<5x+8
Simplify
-1
-3( -1)+4<5( -1)+8
7≮3
- 1/2
- 3( - 1/2)+4<5( - 1/2)+8
11/2 ≮ 11/2
0
-3( 0)+4<5( 0)+8
4 < 8
We can conclude that, as long as x is greater than - 12, the inequality is satisfied. This means our solution is correct.
