What does 5x mean? What does[ggfrac] x/5[/ggfrac] mean?

5x means 5 times x. [ggfrac]x/5[/ggfrac] means x divided by 5.

How can you find the value of x in the expression x + 4 = 5?

I want to get x alone to find out what it is. To get x alone on the left side, subtract 4. Since I always do the same thing to both sides of the equation, I also have to subtract 4 on the right. Then x = 1.

How can you find the value of x in the expression 5x = 20?

5x means 5 times x. I can imagine that there are 5 bags containing cookies and there are 20 cookies in all. Then x represents how many cookies are in each bag. I want to have just one x on the left, which means I have to divide by 5 on both sides. Then x = 4.

What are inverse operations?

Addition and subtraction are inverse operations, and multiplication and division are inverse operations. In 2x = 6, the operation between 2 and x is multiplication, so I have to use division to solve for x.

How can you expand the expression 3(x – 5)?

The 3 on the outside of the parentheses means that everything on the inside gets multiplied by 3. 3 times x is 3x and 3 times 5 is 15. Then the expanded form is 3x – 15.

What are the operations in the equation 4x – 5 = 7? What operations do you need to use to solve for x?

The operations are multiplication and subtraction. So to solve for x, I need to use the inverse operations: division and addition.

To solve 4x – 5 = 7, should you divide first or add first?

I could do either first, but if I divide first, I have to divide 5 by 4 and 7 by 4, which means that I have to work with fractions. That would take longer but still get the right answer. However, if I add 5 to both sides first, then the rest of the solution is much easier.

How can you solve x3-2=2?

[ggfrac]x/3[/ggfrac] means x divided by 3, so the inverse operation is multiplication. I also need to add to isolate the variable. It is simpler to first add 2 on both sides, and then to multiply both sides by 3, but working in the opposite order would also result in the same answer. Then x= 12.

What are two different ways you can solve 2(x – 3) = 8?

Method 1: Distribute 2 across the expression in the parentheses, so that I have 2x – 6 = 8, and then solve by adding 6 to both sides, and then dividing both sides by 2. Method 2: First divide both sides by the factor 2, so that I have x – 3 = 4. Then solve by adding 3 to both sides. Method 2 is more efficient.

To solve 2x + 3 = 5, Sylvia first subtracted 5 from both sides. What did she do wrong?

Because Sylvia did the same operation to both sides, the equation is still correct: the two sides still equal. However, she is no closer to finding out the value of x. She should instead subtract 3 on both sides, which gets her closer to having x alone on the left side.

Solve Algebraic Equations (2-Step)

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What you will learn from this videoWhat you will learn

How to solve algebraic equations in two steps.
That we can solve equations using inverse operations.
That this knowledge can help us start a business, play a concert, and buy fish!

Discussion Questions
- Before Video
  What does 5x mean? What does[ggfrac] x/5[/ggfrac] mean?ANSWER
  - 5x means 5 times x. [ggfrac]x/5[/ggfrac] means x divided by 5.
  How can you find the value of x in the expression x + 4 = 5?ANSWER
  - I want to get x alone to find out what it is. To get x alone on the left side, subtract 4. Since I always do the same thing to both sides of the equation, I also have to subtract 4 on the right. Then x = 1.
  How can you find the value of x in the expression 5x = 20?ANSWER
  - 5x means 5 times x. I can imagine that there are 5 bags containing cookies and there are 20 cookies in all. Then x represents how many cookies are in each bag. I want to have just one x on the left, which means I have to divide by 5 on both sides. Then x = 4.
  What are inverse operations?ANSWER
  - Addition and subtraction are inverse operations, and multiplication and division are inverse operations. In 2x = 6, the operation between 2 and x is multiplication, so I have to use division to solve for x.
  How can you expand the expression 3(x – 5)?ANSWER
  - The 3 on the outside of the parentheses means that everything on the inside gets multiplied by 3. 3 times x is 3x and 3 times 5 is 15. Then the expanded form is 3x – 15.
- After Video
  What are the operations in the equation 4x – 5 = 7? What operations do you need to use to solve for x?ANSWER
  - The operations are multiplication and subtraction. So to solve for x, I need to use the inverse operations: division and addition.
  To solve 4x – 5 = 7, should you divide first or add first?ANSWER
  - I could do either first, but if I divide first, I have to divide 5 by 4 and 7 by 4, which means that I have to work with fractions. That would take longer but still get the right answer. However, if I add 5 to both sides first, then the rest of the solution is much easier.
  How can you solve x3-2=2?ANSWER
  - [ggfrac]x/3[/ggfrac] means x divided by 3, so the inverse operation is multiplication. I also need to add to isolate the variable. It is simpler to first add 2 on both sides, and then to multiply both sides by 3, but working in the opposite order would also result in the same answer. Then x= 12.
  What are two different ways you can solve 2(x – 3) = 8?ANSWER
  - Method 1: Distribute 2 across the expression in the parentheses, so that I have 2x – 6 = 8, and then solve by adding 6 to both sides, and then dividing both sides by 2. Method 2: First divide both sides by the factor 2, so that I have x – 3 = 4. Then solve by adding 3 to both sides. Method 2 is more efficient.
  To solve 2x + 3 = 5, Sylvia first subtracted 5 from both sides. What did she do wrong?
  ANSWER
  - Because Sylvia did the same operation to both sides, the equation is still correct: the two sides still equal. However, she is no closer to finding out the value of x. She should instead subtract 3 on both sides, which gets her closer to having x alone on the left side.
Vocabulary
- Variable DEFINE
- Equals Sign DEFINE
- Equation DEFINE
- Algebraic Expression DEFINE
- One-step equation DEFINE
- Two-step equation DEFINE
- Inverse Operations DEFINE
- Distribute DEFINE
Reading Material
Practice Word Problems
Practice Number Problems
Lesson Plan
Teacher Guide
Assessment
Online Quiz Game Quiz PDF Exit Ticket