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### Course: Class 7>Unit 6

Lesson 8: Solving equations with variable on one side

# Worked example: two-step equations

Sal solves the equation -16 = x/4 + 2. It takes two steps because he first has to subtract 2 from both sides and then multiply both sides by 4. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• cant you just solve this equation by doing the whole thing backwards instead of doing all of this stuff? otherwise, is there a simpler way to solve this
• he kind of overcomplicated this.
• Here is an example:)

Marta gets paid \$15 for each sale, plus a base salary of \$250 per week. Marta wants to earn \$550 this week.

How many sales must she make?
Define a variable for the unknown.
Let x = number of sales
Write an expression that models the problem (in this case, how Marta's weekly pay is calculated).
15x + 250
Set the expression equal to the final result.
15x + 250 = 550
• X=20, this is the correct answer
• In this example, why would we divide first then subtract? 30=5(x+1)
• Use the order of operations (or GEMS): Grouping symbols, Exponents, Multiplicatives (Multiplying and dividing), and Subtractives (Subtraction and addition)
(1 vote)
• What if there are two variables on one side, ( e.g. -20=-4x-6x)
• If they are the same variables, just add or subtract them to get -4x - 6x = -10x. Then your equation simplifies to -20 = -10x → x = 2.
• Anyone knows why we have to subtract on both sides
• An equation acts like the scale/balance in science class. To keep the scale in balance, we always do the same operation to both sides of the equation when we move items across the equals symbol.

There are videos on this back in the lessons on 1-step equations.
Hope this helps.
• How would you do -11b+7=40 ?
• Two steps: Closest to the b is multiply by -11 and then add 7, so going backwards, subtract 7 from both sides and divide by -11. (40-7)/(-11).
• So basically everything has to be equal? Also how would you rewrite -16=x/4+2 so the = is at the end?😕🤔
• -16=x/4+2
-16-2=x/4
-18=x/4
-18*4=x
-72=x
x=-72
Hope this helped!
• How would you solve w+7/4=4
• You would subtract 7/4 from both sides.
You then will need a common denominator to do 4 - 7/4.
Hope this helps.
• so if i am correct for the problem -4(w+1) = -24
(1 vote)
• Yes, the answer is 5. You can confirm this yourself by substituting 5 into the equation in place of w. Then see if the 2 sides are equal. If they are, then you have a good solution. If the sides are not equal, then you have a math error either in finding the original solution or in your check.
• what if the question was -30= 5(x+1)? How would I solve that?
(1 vote)
• -30 = 5(x+1) [We open the bracket]
-30 = 5x+1 [Transposition method]
-30-1 = 5x
Therefore,
-31/5 = x
Have an amazing day, I hope this helped
Thank you!