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Solve Algebraic Equations (2Step)
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 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 VideoWhat 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.
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 VideoWhat 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.
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.
 Onestep equation DEFINE
An equation that requires only one operation to isolate the variable.
 Twostep 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

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