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Find Solutions to Algebraic Inequalities
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What you will learn from this videoWhat you will learn
- That an algebraic inequality is a comparison that contains a variable.
- How to solve algebraic inequalities using inverse operations.
- How this knowledge can help us visit a theme park, pack for a trip, and determine how much we earn at a job!
- Discussion Questions
Before Video
How do you solve the equation 5x=30?ANSWERI divide both sides by 5 to get x=6.
First I subtract 3 from both sides to get [ggfrac]x/2[/ggfrac]=2, and then I multiply both sides by 2 to get x=4. I use inverse operations to solve for the unknown variable.
I can use substitution. Once I find the value of x, I can substitute the value for x in the equation and see if both sides are equal. [ggfrac]4/2[/ggfrac]+3=5, so I know that 2 is the correct value for x.
ANSWERLess than and greater than. 6 < 8 and 8 > 6.
Students draw a number line with an open point at 5 and the arrow traveling right infinitely. There is not only one possible value for x. Any value that is greater than 5 makes this inequality true. x can be 6, 7, 9.6, 100, or many other values.
After Video
Which of the following numbers are part of the solution set for x>13? 10, 12, 13, 14, 17ANSWEROnly 14 and 17. x must be greater than 13, so 13 and all smaller numbers are not part of the solution.
ANSWER15, 16, and 17. Since x must be less than or equal to 17, 17 itself is part of the solution set.
To solve, I treat the > like an equal sign and use inverse operations to solve. Since x is multiplied by 2 and then 3 is added to it, I subtract 3 on both sides and then divide both sides by 2 to get x>2.
Since x is divided by 3 and then 4 is subtracted from it, I first add 4 to both sides, and then multiply both side by 3, to get x≤15.
I can check by substitution. Substituting 6 for x, I get [ggfrac]6/3[/ggfrac]-4≤1, which simplifies to -2≤1. Since -2 is less than or equal to 1, I know that 6 satisfies the inequality.
- Vocabulary
- Equation DEFINE
Two expressions that have equal value separated by a = sign.
- Inequality DEFINE
A comparison between two amounts using symbols like < and >.
- Algebraic inequality DEFINE
An inequality that has a variable.
- Variable DEFINE
A symbol, like x, used to represent an unknown value.
- Inverse operations DEFINE
Multiplication and division are inverse operations, and addition and subtraction are inverse operations.
- Substitution DEFINE
Plugging in values for x to check if they satisfy an equation or inequality.
- Solution of an equation DEFINE
A value that, when substituted into an equation, yields equal values on both sides of the equal sign.
- Solution set of an inequality DEFINE
A set of values that, when substituted into an inequality, yield a true comparison.
- Equation DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide