Algebra 2
1.5 /1.6 Inequality Notes
Example 1: y  6  3
Name______________________________________
Graph the solution on a number line.
The solution set of an inequality can be expressed using set builder notation. For example, the solution set for this
problem can be expressed as _______________________________
You Try: 5w  3  4w  9
Graph the solution on a number line.
Multiplying or dividing each side of an inequality by a positive number does not change the truth of the inequality.
However, multiplying or dividing each side of an inequality by a negative number requires that the order of the
inequality be reversed. For example, to reverse  replace it with  .
Example 2: Solve  4.2x  29.4
Graph the solution on a number line.
You Try:  9.2 y  23
Graph the solution on a number line.
Example 3:  4c 
5c  58
6
You Try:  6(4v  3)  2(10v  3)
Graph the solution on a number line
Graph the solution on a number line.
Algebra 2
1.5 /1.6 Inequality Notes
Name______________________________________
Example 4: Enrique’s company pays Sam to advertise on Sam’s website. Sam’s website earns $15 per month plus $0.05
every time a visitor clicks on the advertisement. What is the least number of clicks per month that Sam needs in order
to earn $50 per month or more?
You Try: Rosa’s cell phone plan cost her $50 per month plus $0.25 for each minute she goes beyond her free minutes.
How many minutes can she go beyond her free minutes and still pay less than a total of $70?
A compound inequality consists of two inequalities joined by the word and or or. To solve a compound inequality you
must solve each part of the inequality.
The graph of a compound inequality containing and is the intersection of the solution sets of the two inequalities.
Example 5: 8  3 y  7  23
Method 1:
Method 2:
Graph the solution set on a number line.
You Try: 10  3 y  2  19
Graph the solution set on a number line.
The graph of a compound inequality containing or is the union of the solution sets of the two inequalities.
Example 6: k  6  4 or 3k  14
Graph the solution set
Algebra 2
1.5 /1.6 Inequality Notes
You Try: x  3  2 or  x  4
Name______________________________________
Graph the solution on a number line.
Example 7: Solve each inequality. Graph the solution set on a number line.
a)
x 3
b) x  5
You Try: Solve each inequality. Graph the solution set on a number line.
a)
t 6
b) u  2
Example 8: Solve 6 y  5  13
Graph the solution set on a number line.
You Try: Solve 2 x  2  4
Graph the solution set on a number line.
You Try: Solve 5z  2  17
Graph the solution set on a number line