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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?ANSWER5x means 5 times x. [ggfrac]x/5[/ggfrac] means x divided by 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.
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.
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.
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?ANSWERThe operations are multiplication and subtraction. So to solve for x, I need to use the inverse operations: division and addition.
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.
[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.
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.
ANSWERBecause 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
A symbol, like x, that represents an unknown quantity.
- Equals Sign DEFINE
Tells us that the expressions on either side have the same value.
- Equation DEFINE
Two expressions that are equal to each other separated by an equal sign.
- Algebraic Expression DEFINE
An equation that uses one or more variables.
- One-step equation DEFINE
An equation that requires only one operation to isolate the variable.
- Two-step equation DEFINE
An equation that requires two operations to isolate the variable.
- Inverse Operations DEFINE
Operations that do the opposite of each other. Addition and subtraction are inverse operations, and multiplication and division are inverse operations.
- Distribute DEFINE
To multiply the number in front of an expression in parentheses by everything inside the parentheses.
- Variable DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide