How do you solve the equation 5x=30?

I divide both sides by 5 to get x=6.

How do you solve the equation [ggfrac]x/2[/ggfrac]+3=5?

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.

How can you check to make sure that x=4 is the right solution to [ggfrac]x/2[/ggfrac]+3=5?

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.

What do the < and > symbols mean? Can you give an example of how to use them?

Less than and greater than. 6 < 8 and 8 > 6.

How can you represent x>5 on a number line? Is there only one value of x that satisfies this inequality?

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.

Which of the following numbers are part of the solution set for x>13? 10, 12, 13, 14, 17

Only 14 and 17. x must be greater than 13, so 13 and all smaller numbers are not part of the solution.

Which of the following numbers are part of the solution set for x≤17? 15, 16, 17, 18, 19

15, 16, and 17. Since x must be less than or equal to 17, 17 itself is part of the solution set.

How can you solve 2x+3>7?

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.

How can you solve [ggfrac]x/3[/ggfrac]-4≤1?

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.

Is 6 part of the solution set for [ggfrac]x/3[/ggfrac]-4≤1?

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.

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?ANSWER
 - I divide both sides by 5 to get x=6.
 How do you solve the equation [ggfrac]x/2[/ggfrac]+3=5?ANSWER
 - 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.
 How can you check to make sure that x=4 is the right solution to [ggfrac]x/2[/ggfrac]+3=5?ANSWER
 - 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.
 What do the < and > symbols mean? Can you give an example of how to use them?
 ANSWER
 - Less than and greater than. 6 < 8 and 8 > 6.
 How can you represent x>5 on a number line? Is there only one value of x that satisfies this inequality?ANSWER
 - 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, 17ANSWER
 - Only 14 and 17. x must be greater than 13, so 13 and all smaller numbers are not part of the solution.
 Which of the following numbers are part of the solution set for x≤17? 15, 16, 17, 18, 19
 ANSWER
 - 15, 16, and 17. Since x must be less than or equal to 17, 17 itself is part of the solution set.
 How can you solve 2x+3>7?ANSWER
 - 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.
 How can you solve [ggfrac]x/3[/ggfrac]-4≤1?ANSWER
 - 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.
 Is 6 part of the solution set for [ggfrac]x/3[/ggfrac]-4≤1?ANSWER
 - 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
- Inequality DEFINE
- Algebraic inequality DEFINE
- Variable DEFINE
- Inverse operations DEFINE
- Substitution DEFINE
- Solution of an equation DEFINE
- Solution set of an inequality DEFINE
Reading Material
Practice Word Problems
Practice Number Problems
Lesson Plan
Teacher Guide
Assessment
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