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Learn it your way
A short class with Sarah and her students. The other ways are under More.
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Today, we will delve into linear equations in one variable. Can anyone tell me what they think a linear equation is?
Is it an equation that has a straight line when graphed?
Exactly! Linear equations are represented graphically as straight lines. They consist of variables raised to the first power. For example, 2x + 5 = 10.
What does it mean for an equation to have one variable?
Great question! An equation with one variable means that it only contains one type of variable, like x or y. In our example 2x + 5 = 10, x is our single variable.
To simplify, remember the acronym 'LIN' - Linear, Involves one variable, and No exponents greater than one. Everyone got that?
Got it! LIN helps me remember.
Following our introduction, let’s see a simple problem. If x + 3 = 7, how do we find x?
We subtract 3 from both sides!
Correct! That gives us x = 4. Well done!
Now, let's tackle equations like 2x - 3 = x + 2, which have variables on both sides. Who can suggest how we might approach this?
We could try moving the variables to one side.
Exactly! We subtract x from both sides. Let’s do it step by step: we get 2x - x - 3 = 2.
So that simplifies to x - 3 = 2.
Correct! Now how do we solve for x?
Add 3 to both sides to find x = 5.
Fantastic! Remember the phrase 'SIMPLIFY AND SOLVE' to help you remember our approach!
I find that helpful!
Great! Let’s do another similar example. Try 5x + 7 = 3x - 5.
Next, we will discuss simplifying equations before solving them. Can anyone give me an example of what that might look like?
What about when we have fractions? They can make it tough.
Absolutely! For example, consider the equation 6(x + 1/2) = 3.
We could multiply everything by 2 to eliminate the fraction!
Exactly! Multiplying through by 2 gives us 12(x + 1) = 6, simplifying our work considerably.
Doesn't that mean balancing the equation too?
Correct! Whatever we do to one side, we must do to the other to maintain the equality. Remember to always 'BALANCE' your operations.
Sounds good! I'll keep that in mind when I'm solving.
Linear equations might sound a chore, but with 'solve and balance', you'll never bore!
Once upon a time, in Equatia, there lived a wise old mathematician who said, 'To solve an equation, keep both sides equal - treat them as best friends.'
Remember 'SOLVE': Separate, Operate, Leave variable alone, Verify solution, Eliminate mistakes.
Use 'L.E.S.S.' to remember - Linear equations, Equal sign, Simplifying expressions, Solve for variable.
Term
What is a linear equation?
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Term
What does RHS stand for?
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An equation involving a variable raised to the first power.
A symbol used to represent an unknown value in an equation.
A combination of numbers, variables, and operations without an equality sign.
The expression on the left side of the equality sign in an equation.
The expression on the right side of the equality sign in an equation.
This section introduces linear equations in one variable, explaining their characteristics and methods for solving them.
In this section, students revisit algebraic expressions and equations, focusing specifically on linear equations in one variable. The section outlines how to identify linear expressions, demonstrates solving equations involving variables on both sides, and emphasizes techniques for simplifying equations to find solutions.
In this section, we explore linear equations in one variable, which are characterized by their linear nature, meaning the variable involved has an exponent of one. We differentiate between algebraic expressions (like 5x and 2x - 3) and equations (where an equality sign = is present).
Key Aspects Covered:
2x - 3 = x + 2, students learn to isolate the variable through transposition and addition or subtraction of terms.By mastering these techniques, students will be equipped to tackle various mathematical problems involving linear equations effectively.