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## Operations and Algebraic Thinking 229+

### Unit 1: Lesson 2

Linear equations with parentheses

# Equations with parentheses

Sal solves the equation -9 - (9x - 6) = 3(4x + 6) using the distributive property. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• 4r−3=3(3r+4)
I am older than most trying
To learn algebra II
To help my grandkids,
H
Very old school ...
Is there a way to find
Out the value of the letters
In various problems
For example the above
Problem
What value is the r
• We can do this in steps:

First, we need to open the parenthesis.

4r-3 = 3(3r+4)

4r-3 = 9r+12

Then, we can either add 3 to both sides or subtract 12 to get only R's on one side, like this:

4r-3 = 9r+12

4r = 9r+15 or 4r-15 = 9r

Then, we subtract the extra R's.

4r = 9r+15 or 4r-15 = 9r

0 = 5r+15 or -15 = 5r

If you chose the options on the left, you subtract 15 from both sides to get the equation on the right. Then, you divide by 5 to get the value for r:

-15 = 5r

*-3 = r*

Hope this helps!
• Hi!

What if we were dealing with Inequalities? Would having a negative 9 behind the brackets change the direction of the Inequality?

Here, have a look:

-9 times [9x - 6] > 3 times [4x + 6] » Would that initial negative 9 have influence on the direction the Inequality assumes? Instead of having ''greater than'', would we have ''lesser than''? Or do we turn a blind eye to that initial negative 9 and only change the direction of the Inequality if, later on, we need to multiply or divide?

Hope I explained myself properly.

Cheers!
• I really don’t understand what this guy is talking about
• why cant you do -9-1 before you use the distributive property in the beginning of the equation?
• PEMDAS rules always apply when you are simplifying each expression on the sides of the equation.
You can't do the work inside the parentheses because you can't combine unlike terms. But, you have to deal with the parentheses. The only way to remove the parentheses is to use the distributive property.

If you do -9-1 as your 1st step, you are skipping all the PEMDAS rules prior to additionn/subtraction, which can't be done.

Hope this helps.
• what if the the variables are the same value
• They are supposed to be. In this case, Sal is only solving for one variable: x. Even though x appears twice in the equation, x is one number. Just like 9 appears twice, and 6 appears twice, x appears twice but it's one number still. Hopefully that makes sense.
• Is there a way to memorize all of these steps to the linear equations?
• well use the BODMAS(Bracket, Of, Division, Multiplication, Addition, Substraction) rule. it helps, don't memorize maths.
eg.
solve 18-(20-15/3)
=18-(20-5)
=18-15
=3 (ans)
• How do you know if it is negative and not just subtraction? At point 50 seconds in the video he says negative one times negative six. How would you know it's not just subtraction?
• If you mean something like -7(-3), I can answer that. There are three ways to indicate multiplication: an x sign, a dot, or a number in parentheses touching another number. If it is not one of those, and is more like -5-6, then it would be subtraction. Hope this helps!
• what does parenthesis mean?
• parenthesis are '(' and ')' . Calculations between () or parenthesis have the highest priority when it comes to sequencing.
• What do I do when I have a problem like 5(x➗5-3)=30. I can't get the right answer. I come up with 60.
• Here is a step by step solution to 5(x➗5-3)=30
1. Divide both sides by 5, which gives *(x➗5-3)=6*
2. Add both sides by 3: x➗5=9
3. Multiply both sides by 5: x=45

P.S. if you are able to list the steps you use in solving the equation, then I might be able to help you in explaining why you obtain 60 as your answer.
• how do i do this 8(10-k)=k
• first distribute 8 to parenthesis
80-8k = k
80 = 9k
divide by 9
80/9 = k
8.888 = k
• Hi I am going to 7th grade and going to be learning algebra 1 what are some tips I can use to help me understand this topic more.
• Great question, and smart of you to prepare!

Algebra uses and builds upon all past Arithmetic math skills and concepts, and both are used in Geometry.

It's very useful in life and is applied in many different situations, so we can find the answers we need.

Algebra is a method to solve for unknown values, using logic, balance, and Arithmetic.

so…
Review Arithmetic, (algebra is full of fractions, exponents, signed integers, etc), and…