Vocabulary
Inverse Operation- using the opposite operation to solve the equation.
Examples
Equations and Inequalities - Two-step equations and inequalities - First Glance. It takes two steps to solve an equation or inequality that has more than one operation: Simplify using the inverse of addition or subtraction. Simplify further by using the inverse of multiplication or division.
Now we'll solve some more complicated equations and inequalities - ones that have two-step solutions, because they involve two operations. Remember, solving equations is like solving a puzzle. Just keep working through the steps until you get the variable you're looking for alone on one side of the equation.
Here's a two-step equation. Let's start with the variable x, and describe, step by step, what is being done to x in an equation.
| 3x - 10 = 14 |
Equation |
| 3x | First, x is multiplied by three. |
| 3x - 10 | Next, ten is subtracted from the term 3x. |
| 3x - 10 = 14 | We get a result of 14. |
|
Start
with x --> Multiply by 3 --> Subtract 10 -->
Result is 14. |
|
Solving
an equation is like running the equation backwards to discover what number
will work in the equation. Now let's work backwards and use inverse operations
to undo all the steps. We can start with the result of 14.
|
14
|
Start
with result. |
|
14
+ 10
|
Next, working backwards, we can add 10, which is the inverse of subtracting 10. |
|
14 + 10 3 |
Now we divide by 3, since that's the inverse of multiplying by 3. |
|
24
= 8
3 |
We get
an answer of 8. |
|
Start
with result of 14 —> Add 10 —> Divide by 3
Answer is 8. |
|
Do
you see how it's important when solving an equation to "undo"
all the steps in the correct order? No matter how many steps are in the
original equation, you can work backwards and apply the inverse operations,
in order, to arrive at the solution!
You can solve
two-step inequalities in exactly the same way. Just work backwards, using
the inverse operations, to arrive at the solution. But watch out when multiplying
or dividing by a negative number! Just as you learned in the last lesson,
you must reverse the inequality symbol.
http://www.math.com/school/subject2/lessons/S2U3L6EX.html
Video Help
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/v/why-we-do-the-same-thing-to-both-sides-two-step-equations
https://www.youtube.com/watch?v=9ITsXICV2u0
https://www.youtube.com/watch?v=jExsRDEO0gU
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