Loading the lesson
Loading the lesson
Search AllRounder.ai
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Learn it your way
A short class with Sarah and her students. The other ways are under More.
Sign up free to listen. Transcripts are free to read.
Today, we're going to learn about solving equations with variables on both sides. Can anyone give an example of such an equation?
How about 2x - 3 = x + 2?
Exactly! In this case, both sides contain the variable x. The goal is to isolate the variable. Can anyone tell me how we might begin solving this?
We can subtract x from both sides?
Good thinking! That's a great first step. When we subtract x, what do we get on each side?
We get 2x - x - 3 = 2.
Right! Now, can someone simplify this further?
That gives us x - 3 = 2.
Excellent! Now, what’s the next step?
Add 3 to both sides, so we get x = 5.
Perfect! Remember, we always need to do the same operation on both sides to keep the equation balanced.
Let’s look at a more complex example: 5x + 7/2 = x - 14. What’s our first step?
We could multiply by 2 to eliminate the fraction!
Exactly! Multiplying both sides by 2 gives us a simpler equation. What do we get?
That becomes 10x + 7 = 2x - 28.
Great! Now, how do we isolate x from here?
We can subtract 2x from both sides.
Correct! And what does that lead us to?
It simplifies to 8x + 7 = -28.
Now, what’s our next move?
We subtract 7 from both sides to get 8x = -35.
Fantastic! Finally, how do we find x?
We divide by 8, giving us x = -35/8.
Absolutely right! This method of manipulating both sides is key in solving these equations.
To keep the balance, let's not lose, do the same to both, that's the right move!
Once there was a magician named Variable who loved to play games. He would always keep EQUALITY balanced by doing the same trick on both sides of his magic equation.
Remember: I.S.O.L.A.T.E - Isolate, Subtract, Or, Leave Alone The Equation!
MATH - Move All Terms Homogeneously.
Term
What is an equation?
Click to flip
Term
What does it mean to isolate a variable?
Click to flip
This section focuses on solving equations with variables on both sides, detailing methods and providing examples.
In this section, we learn how to solve equations where variables are present on both sides. We explore various methods to manipulate these equations, illustrated by examples that show the step-by-step process to isolate the variable and obtain solutions.
An equation represents the equality of the values of two expressions, such as in the example 2x - 3 = 7. Here, the left-hand side (LHS) and the right-hand side (RHS) can also include variables, as demonstrated in 2x - 3 = x + 2.
To solve these equations, we need to isolate the variable. The section introduces how to manipulate both sides of the equation. For example, in the equation 2x - 3 = x + 2, steps such as subtracting x from both sides help us to eventually isolate x as shown in the solution where it simplifies to x = 5.
Additional examples, such as 5x + 7/2 = x - 14, illustrate multiplying each side of the equation to simplify the expressions further. The section emphasizes understanding the operations performed on both sides to maintain equality and reach the solution effectively.
Example 2: Solve
Solution: We have
or
or
(solution)