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ALGEBRA 1
Lesson 3-5 Warm-Up
ALGEBRA 1
Lesson 3-5 Warm-Up
ALGEBRA 1
“Compound Inequalities” (3-5)(3-1)What is a compound
inequality?Compound Inequality: two inequalities that are joined by the word and or the word or - A compound inequality joined by the word and means any number that makes both inequalities true.
Example: x ≥ 5 and x ≤ 7 means “x is greater than or equal to -5 and less than or equal to 7”. It can also be written as -5 ≤ x ≤ 7 which means “x is between -5 and 7 inclusive (including those two values)”
ALGEBRA 1
Write a compound inequality that represents each
situation. Graph the solutions.
a. all real numbers that are at least –1 and at most 3.
b –1 and b 3 –1 b 3 > < < <
b. all real numbers that are less than 31, but greater than 25.
n < 31 and n > 25 25 < n < 31
Compound InequalitiesLESSON 3-5
Additional Examples
ALGEBRA 1
“Compound Inequalities” (3-5)(3-1)How do you solve a
compound inequality in which there are three parts (two inequality signs) joining the inequalities with “and”?
Method 1: You can solve a compound inequality by splitting it up into two inequalities joined by and. Then, isolate the variable for each inequality.
Example: Solve -4 r – 5 ≤ -1.
-4 r - 5 and r – 5 ≤ -1
4 + 5 r - 5 + 5 and r – 5 + 5 ≤ -1 + 5 Add 5 to both inequalities.
1 r and r ≤ -4 Simplify
1 r ≤ 4 Combine the inequalities
Method 2: You can solve a compound inequality by isolating the variable by working on all three parts at the same time.
Example: Solve -4 r – 5 ≤ -1. Graph the result.
-4 r – 5 ≤ -1
-4 + 5 r – 5 + 5 ≤ -1 + 5 Add 5 to all three parts of the inequality.
1 r ≤ 4 Simplify
ALGEBRA 1
Solve 5 > 5 – f > 2. Graph the solution.
5 – f – 5 > 2 – 5
–f > –3
5 – 5 > 5 – f – 5
0 > –f
5 – f > 25 > 5 – f
f < 30 < f
Write the compound inequality as two inequalities joined by and .
and
0 < f < 3
and
0–1
–f–1<
–3–1
–f–1 <
Compound InequalitiesLESSON 3-5
Additional Examples
ALGEBRA 1
Your test grades in science so far are 83 and 87. What
possible grades g can you make on your next test to have an
average between 85 and 90?
Words: the averagewhich is less
than or equal tois less thanor equal to
85 90
Equation: 85 90< 83 + 87 + g 3
g<
Compound InequalitiesLESSON 3-5
Additional Examples
ALGEBRA 1
(continued)
85 < 83 + 87 + g 3
< 90
< <255 170 + g 270 Simplify.
< <255 – 170 170 + g – 170 270 – 170 Subtract 170.
< <85 g 100 Simplify.
The third test grade must be between 85 and 100, inclusive.
Compound InequalitiesLESSON 3-5
Additional Examples
Multiply by 3.3(85) < < 3(90)83 + 87 + g 33
ALGEBRA 1
“Compound Inequalities” (3-5)(3-1)How do you solve a
compound inequality in which two inequalities are joined by the word “or”?
A compound inequality joined by the word or means any number that makes either inequality true.
Example: -5 is a solution to the following compound inequality, because it is a solution to one of the inequalities (x < -3)
ALGEBRA 1
Write an inequality that represents each situation.Graph the solutions.
a. all real numbers that are less than 0 or greater than 3.
n < 0 or n > 3
b. Discounted tickets are available to children under 7 years old or to adults 65 and older.
a < 7 or a 65; because age cannot be negative, a ≥ 0.>
Compound InequalitiesLESSON 3-5
Additional Examples
ALGEBRA 1
Solve the compound inequality 3x + 2 < –7 or –4x + 5 < 1.
Graph the solution.
3x + 2 – 2 < –7 – 2
3x < –9
<3x3
–93
–4x + 5 – 5 < 1 – 5
–4x < –4
>–4x–4
–4–4
3x + 2 < –7 –4x + 5 < 1
x < –3 x > 1
or
or
Compound InequalitiesLESSON 3-5
Additional Examples
ALGEBRA 1
1. Write two compound inequalities that represent the given situation. Graph the solution.all real numbers that are at least 2 and at most 5
2. Write an inequality that represents the given situation. Graph the solution.all real numbers that are less than –3 or greater than –1
3. Solve –2 2x – 4 < 6. Graph the solution.
4. Solve 3x – 2 < –8 or –2x + 5 3. Graph the solution.
<
<
b 2 and b 5, 2 b 5> < < <
n < –3 or n > –1
1 x < 5<
>x < –2 or x 1
Compound InequalitiesLESSON 3-5
Lesson Quiz
