MATH 3
Nov 14
Solving simple equations.
Today we’ve learned how to solve simple linear equations.
Here is the short summary of what we did in class :
Balance
The most important thing to remember when solving the equation is to always do
the same thing to both sides of the equation. This is called balance.
For example, if you add a number on the left side of the equation, then you also
must add the same number to the right side of the equation.
x=3
x+2=3+2
x+2=5
Keeping things in balance also works for subtraction, multiplication and division.
Here is a multiplication example.
p=5
2•p=2•5
2p = 10
When you take higher level math classes you will learn about more math
operations that can be used when solving equations. For all the operations, you
need to remember the concept of balance.
Opposites
When solving equations, doing the opposite operation is usually required.
By doing the opposite you undo operations that have been done to the variable.
For example, you equation was
x+3=15
That is if you add 3 to x you get 15.
The opposite of adding three is subtracting three. ( for example, if you add three to
100 you get 103. If you then subtract three from 103, you’re back where you
started.)
Adding 3 and subtracting 3 are opposites.
So, we have to subtract 3(remember this has to be done to both sides of the
equation).
x+3-3=15-3
and we get
x=12
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The opposite of subtraction is addition.
The opposite of multiplication is division.
The opposite of division is multiplication.
Now try to solve the following equations:
x-156=344
x+215=347
x-35=648
x+15=132
Homework
1. Solve the equations
x+238=333
x+129=235
x-32=238
x-267=465
Now, try to solve the following equations (remember to apply the 2
principles from the classwork ):
283-x=215
x•5=15
113-x=98
x•6=36
For the next two equations think what they have in common with 2 previous
ones and how this helps solving them.
5•x=15
6•x=36
2. Sum of 6 distinct numbers is equal to 22. What are these numbers?
3. How many two-digit numbers are there with the sum of digits equal to
10?
4. Five students in a math competition got the prizes. The first prize was
awarded for 20 points, the second for 19 points and the third for 18
points. How many students got first, second and third prize if the sum
of all the points they got is 94?
5. Solve the following equations and check the solutions.
(a) x + 4 = 28
(b) x - 9 = 72
(c) 6 + x = 30
(d) x - 3 = 12
(e) 2 +x = 18
6.
 One fish-tank has a fishes, and the other one has b fishes less.
How many fishes are there in fish-tanks in total?
 One strawberry plant has m berries, and another one has n
berries. Out of them, a berries are ripe and red. How many green
berries are there?
 One fish-tank has a fishes. This is b fishes less than in the other
fish-tank. How many fishes are there in total?
 John gathered c apples. First he ate a apples, and then he ate b
apples. How many apples left?
 During the vacations, there were a rainy days, b cloudy days, and
the number of sunny days is the same as the number of rainy days
and cloudy days together. How long were the vacations?
 The first garage had c cars, and the second d cars. In the
morning, a cars left from the first garage, and b cars left from the
second garage. How many cars are left in both garages together?
7. Bunnies cut the logs. How many pieces they get after 10 cuts?
8. Bunnies cut several logs. They made 10 cuts and got 16 pieces.
How many logs were there in the beginning?
9. Bunnies continue cutting the logs. But now, two ends of the log are
fixed. 10 middle pieces fall down, and 2 end pieces stayed fixed.
How many cuts did bunnies make?
10.The round doughnut was cut into pieces. How many pieces were
there after 10 cuts?