Brain Buster Algebra 1d
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This quiz picks up where we left off with Red Hot Algebra 1d.
Note: 2 * 3 is the same as 2 x 3 and 2Y is the same as 2 x Y and 2 * Y
Both sides of an equation are equal to each other 2 + 3 = 5 and 2 + 3 = 1 * 5
Let’s introduce an unknown, 2 + __ = 1 * 5 we can quickly work out the blank is 3
Let’s replace the blank with the varibale Y
2 + Y = 1 * 5
Solve 2 + Y = 1 * 5 for Y is the same as asking what does Y equal.
To solve for Y we need to isolate Y and because both sides of the equation are equal whatever we do to one side we have to do to the other side.
On the left side a 2 is added to Y, the 2 needs to be removed so Y is
by itself. We can subtract 2 from both sides.
2 + Y - 2 = 1 * 5 - 2
Simplify the left side, 2 + -2 = 0 so we are left with Y = 1 * 5 -2
Simplify the right side, 1 * 5 - 2 equals 3 so we are left with Y = 3 and that is it we have solved for Y.
The same logic applies for multiplication and division, whatever you do to one side you have to do to the other.
Y * 4 = 8 would become Y * 4 / 4 = 8 / 4
It is normally easier to start isolating the variable by subtracting or adding before dividing or multiplying. As long as you do the same thing on both sides of the equal sign you can start isolating the variable in any order you like.
Another example: Solve 12 = t + 3 for t.
a. Isolate the t by subtracting 3 from both sides: 12 - 3 = t + 3 -3
b. Simplify both sides: 9 = t + 0
c: The answer is t = 9
Let's take this one step further and what if there is an unknown on both sides of the equation. The first step is to remove one of the unknowns from one of the sides and then the same steps as outlined above are followed. Let's work an example.
Solve 3Q + 6 = 6Q + 3 for Q.
a. We can either subtract 3Q or 6Q from both sides, let's do 3Q so we don't have to deal with negatives. 3Q - 3Q + 6 = 6Q - 3Q + 3
b. Simplify the left side: The 3Q - 3Q cancels out so we are left with 6 = 6Q - 3Q + 3
c. Simplify the right side: 6Q - 3Q equals 3Q so we are left with 6 = 3Q + 3
d. Now we subtract 3 from both sides: 6 - 3 = 3Q + 3 -3
e. Simplify: 3 = 3Q
f. Because 3Q is 3 multiply Q we now need to divide both sides by 3 to isolate the Q so this gives 3 / 3 = 3 /3 * Q
g. This simplifies to 1 = Q
Now let’s work a word problem
If a laptop costs twice as much as an iPad and the total for both is $1350 what is the price of the iPad?
We want to calculate what the price of the iPad is but all we know is that the total is $1350 and the laptop is 2 times the price of the iPad.
As a first step let’s introduce a variable and say the price of the iPad is equal to P
We know that the laptop price is 2 times the iPad price so we can say that the laptop costs 2 * P
This is great so now we have a variable for both of them and we also know that the price of the iPad and the price of the laptop equals $1350
So we can put an equation together and we get: P + 2P = 1350
We can simplify to: 3P = 1350
Now all we have to do is isolate P by dividing both sides by 3
Which is P * 3 / 3 = 1350 / 3
The * 3 and / 3 cancel out and we are left with P = 450
So the price of the iPad is $450 and the price of the laptop is $900