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Algebra I Unit Three Review
Graphing inequalities
Be able to graph inequalities after solving.
> greater than; open circle
< less than; open circle
≥
greater than or equal to; closed circle
≤
less than or equal to; closed circle.
If the variable is on the left, graph the solution in the direction of the inequality. Make
sure to graph three numbers, going in ascending order from left to right.
Example:
Graph: x < -3
Graph: x ≥ 6

-4
-3
-2
5
6
7
If the variable is on the right, go in the opposite direction.
Example:
Graph: 8 > x
Graph: -6 ≤ x

7
8
9
-7
-6
-5
Solving inequalities
Be able to solve one-, two-, and multi-step inequalities. Solve inequalities in the same
manor as solving equations. The difference is the inequality sign. Make sure to change
the direction of the inequality when multiplying or dividing by a negative (the
coefficient of the variable is negative)
Solve and graph the following:
1.
y–2≤4
2.
10 ≤ x + 8
3.
6 + d < 11
4.
8x > 56
5.
-3y ≤ 21
6.
x
< -2
7

7.
3
x ≥ -9
5
8.
3x + 2 < 2x + 5
9.
2(3 – x) ≥ 14
10.
3x – 5x + 7 ≤ -5

Compound inequalities
“and” compound inequalities are two inequalities joined by the word “and” or one
combined inequality that has two inequality symbols with a variable or variable
expression in the middle. The solution to an “and” compound inequality must be true
for both inequalities. The graph of an “and” inequality looks like one of these,
depending on the inequality symbol used:


 
“or” compound inequalities are two inequalities joined by the word “or”. The solution
to an “or” compound inequality must be true for one of the inequalities. The graph of
an “or” inequality looks like one of these, depending on the inequality symbol used:
 


Solve compound inequalities by isolating the variable and using the same rules used
earlier in solving inequalities. When graphing, you only need to graph two numbers.
Solve and graph the following compound inequalities:
1.
x + 5 ≤ -4 or -2x < 6
2.
x – 2 ≥ -6 and 5 + x < 7
3.
-3 ≤ x + 1 < 3
4.
x – 2 ≤ -6 or 5 + x > 7
Absolute value equations and inequalities.
For absolute value equations, remember that whatever is in the absolute value sign can
be a positive or negative value of what it equals. You will always have 2 answers. If
the variable is alone or is multiplied by a coefficient, you will have opposite answers. If
the variable has something added or subtracted to it, there will be two totally different
answers.
Solve the following absolute value equations:
1.
x 5
2.
3x  12
3.
x  4  10
 For absolute value inequalities,
 you will solve them by setting
them up as compound
inequalities depending on the inequality symbol. For greater than or greater than or
equal to (> ≥), set them up as “or” compound inequalities, solve and then graph. For
less than or less than or equal to (< ≤), set them up as “and” inequalities, solve and then
graph. When setting up the two inequalities to solve, write one just as it is written but
without the absolute value sign and then flip the inequality symbol and change the sign
of the number for the second inequality. Then solve the compound inequalities and
graph.
Solve and graph the following absolute value inequalities.
1.
x ≥7

x < 11
4.
x5 < 9

3.

2.
x3 ≥8

Word Problems
Remember to set up the inequality with the variable expression on the left, then the
inequality symbol, then the number.
Some key words and the symbols they represent
at least ≥
no less than ≥
minimum ≥
at most ≤
no more than ≤
maximum ≤
Set up an inequality and solve for the following.
greater than >
less than <
1.
The sum of three consecutive odd integers is less than 100. What are the greatest
possible values of these three integers?
2.
What is the greatest number of $.42 stamps you can buy for $10.00?
3.
Suppose that you have $50 to spend at the mall. You spend $24.50 at Claire’s.
How much more money do you have to spend for the day?
4.
You have a job working at the driving range. Your pay is $6.75 per hour. How
many full hours must you work to earn at least $150?