8.EE.7 Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Collecting Like Terms
The first skill we learn in this unit is how to combine like terms. In order to combine them, we need to know what they are:
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Now, you try:
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Try again:
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Now that we know what they are, how do we combine (add) them together?
Distributive Property
Our next goal is to master the distributive property. First, we must understand what it is. The distributive property is a rule that we use when we need to multiply an expression.
Examine the following chart and videos to learn more about this property.
Examine the following chart and videos to learn more about this property.
Solving Equations:
Two Step
Let's get to solving some equations!! We should begin by reviewing two step equations:
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Solving Equations:
Using the Distributive Property
Let's use what we have learned and apply it to solving equations.....Here we have two methods to solve for x. Choose the method that you feel most comfortable with. |
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Solving Equations:
Variables on Both Sides
Now that we have our basic moves down......let's try solving with variables on both sides.
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Evaluating Equations
Let's look at evaluating equations with variables on both sides of an equation:
Types of Solutions:
One, Infinite, and No Solutions
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Identify how many solutions by inspection. One Solution: Different slope (number of x's); doesn't matter about the constant No Solution: Same slope (number of x's); different y-intercept (constant or number with no letter) Infinite Solution: Same slope (number of x's); same y-intercept (constant or number with no letter) |
Graphic representation of Types of Solutions:
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