Transcript Solve Inequalities

Inequalities
Today you will learn to:
• graph and write inequalities
• solve inequalities by using properties of inequality
M07.B-E.2.2.2: Solve word problems leading to
inequalities of the px + q > r or px + q < r, where p, q,
and r are rational numbers, and graph the solution set
of the inequality.
Warm-up Problem: Inequalities
Your elementary school is
having a fall
carnival. Admission into
the carnival is $3 and each
game inside the carnival
costs $1. Write an
inequality that represents
the possible number of
games that can be played
having $10. What is the
maximum number of games
that can be played?
What are Inequalities?
A mathematical sentence that contains <, >, ≤,
≥, or ≠ is an inequality. Sometimes (and especially
in this class), an inequality contains a variable, such
as x ≥ 2.
A solution of an inequality is any value that
makes the inequality true. The solution of an
inequality can include many numbers. For
example, 6, 8, and 15 are all solutions of x ≥ 2,
because 6 ≥ 2, 8 ≥ 2, and 15 ≥ 2.
Example: Which number(s) is a solution to x ≥ 5: -3,
0, 2, 5, 7.
Graphing Inequalities
A graph can show all of the numbers in a
solution. For x ≥ 2:
Note: closed circles are used for ≤ and ≥, and open
circles are used for < and >.
You can also write an inequality by analyzing its
graph. Look at the number line below. What
inequality is represented by the number line?
Solve Inequalities
Solving inequalities means finding values for the
variable that make the inequality true. The only
difference between solving inequalities and solving
equations is that equations have an ‘equals’ sign, where
inequalities do not.
You can solve inequalities using properties similar
to those you used when solving equations. Just like
algebraic equations, you will be using inverse
operations to solve inequalities. Consider the
following:
x+2<3
x + 2 – 2 < 3 – 2 (Subtract 2 from both sides)
x<1
This means that any value less than (but not equal
to) 1 will make the inequality true!
Solve Inequalities: Examples
Solve the following inequalities.
A.15x + 7 ≥ -53
B.6d – 11 < 7
A.9(y – 3) ≤ 36
B.10 > 8(s – ¾)