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EXAMPLES & SOLUTIONS
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Inequalities do not have a direct relationship between variables. The values are usually, only being compared.
Inequality word problems are first created as an expression.
They are converted to equations to solve a problem.
The important factor to consider is the direction of the sign.
They are mostly utilized in comparing measurements or distances.
There are a range of solutions to the inequality.
They are NOT equal to each other.
If they are equal, then the values are only being compared to a certain value.
INEQUALITY WORD PROBLEM
Examples and explanations of how to solve inequality word problems
Word Problem
A person had 4 board games last year. The person wants to have at least as many as they had last year.
What is needed to discover the number of board games?
Gathering Information
The variable is the unknown number of board games (n).
The constant is the number of board games they had (4).
The operator is the ">" sign. It means "greater than and equal". At least (4) board games or more are needed.
The coefficient is the number of board games increased per year, (1).
The terms are the unknown number of board games (n), and the initial number of board (4).
Components
Variables: n
Constant: 4
Operator: ">"
Coefficient: 1
Terms: n, 4
Write the Equation
Variable: n
"At least" means: '>'
Initial # of games: 4
n > 4
SOLVE THE INEQUALITY
This equation states that the unknown number of board games (n) is > 4
6
7
-2
at least 4 or more
3
4
5
2
-1
0
1
-3
-7
-6
-5
-4
THE PERSON NEEDS AT LEAST FOUR (4) GAMES OR MORE TO HAVE AS MANY GAMES AS BEFORE
therefore,
ANY NUMBER GREATER AND EQUAL TO FOUR (4) WILL SOLVE THE EQUATION.
Fact: Inequality problems have more than one possible solution.
Word Problem
A person wants to fill a 32 ounce water jar until it overflows. The current amount of water in the jar is 17.5 ounces. How much water is needed to overflow the jar?
What is needed to discover how much water will overflow the jar?
Gathering Information
The variable is the unknown amount of water needed to overflow the jar (w).
The constant is the total ounces of water in the jar (32) & the current ounces of water (17.5) in the jar.
The operator is the "+" sign. It means to 'add together'. The initial ounces of water (17.5) and the unknown amount of water (w) are added togther.
The operator is the ">" sign. It means 'greater than'. The combined initial ounces (17.5) and the unknown ounces of water (w) must be 'greater than', 32 ounces to overflow the water in the jar.
The coefficient is the number of board games increased per year, (1).
The terms are the current amount of water (17.5), the total amount of liquid to overflow the jar ( > 32 ounces) and the unknown amount to overflow the jar (w).
Components
Variable: w
Constant: 17.5, 32
Operator: '+', '>'
Terms: 17.5, 30, w
Coefficient: 1
Expression:
17.5 + w
Write the Equation
Initial jar content: 17.5
"Add together" means: '+'
Variable: w
"Greater than" means: '>'
Amount to overflow: 32
17.5 + w > 32
SOLVE THE EQUATION
17.5 + w > 32
17.7 -17.5 + w > 32 - 17.5
0 + w > 14.5 w > 14.5
-28
-24
-20
-16
-12
-8
-4
0
4
8
12
16
20
24
28
14.5
A PERSON NEEDS MORE THAN (14.5) OUNCES BEFORE THE JAR OVERFLOWS
therefore,
ANY NUMBER GREATER THAN 14.5 WILL SOLVE THE EQUATION.
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