Solving Equations

one and two step equations

Get out paper and pencil

To solve an equation you have to set out to meet one very important goal.

The variable(letter) has to be by itself on one side of the = sign and all the constants(numbers) should be on the other side

Equations must maintain balence or they fall apart.

if we do an operation to one side of the equal sign, we must do the same operation to the other side.

The original problem is 5 + x = 3

we need that 5 to goto the other side.

The opposite operator of + 5 is - 5.

Notice how when we subtract -5 from both sides, 5-5 on the left becomes 0. this achieves our goal of getting x by itself.

 $\ \frac{m}{4}=3$  

notice it says, m divided by 4 on the left side, to get m by itself we use the opposite operator. multiply is the opposite of division. if we multiply both sides by 4 that will get the m by itself on the left. 

Look at these four examples and notice how the opposite operation is used to get the variable by itself.

get ready to try it yourself!

Multiple Choice

What will you do to solve this equation?

X + 6 = 3

• subtract 6 from both sides

• add 6 to both sides

• subtract 3 from both sides

• add 3 to both sides

Multiple Choice

What will you do to solve this equation?

4x = 16

• divide both sides by 4

• multiply both sides by 4

• subtract 4 from both sides

• divide both sides by 16

why do you learn math? so you can use it to do more math.

did you learn these basic concepts?

i hope so because you might have to use them in a combo solution.

What about a fraction as a coefficient? you can do the operations one at a time.

notice we have 8/4 as the coefficient. we can multiply both sides by 4 to get a new coefficient of 8. then we can divide by 8 to get the variable by itself.

It turns out there is a neat rule, if you multiply a fraction by its reciprocal(flip the fraction) it = 1

So the other way to solve a fraction coefficient is to multiply by the reciprocal of the coefficient to both sides. That will also get the variable by it self. pick what method seems easier to you. Which method will you pick? Try one...

Multiple Choice

 $\frac{3}{2}x\ =6$  solve for x

• 4

• 3

• 12

• 2

Notice we have a coeffecent and a constant on the same side as X.

We still want to get X by itself.

We should do any adding or subtracting first, to get the constant on the other side of the = sign, then use multiply or divide to get the coefficient to the other side.

The order in which you solve can save time.

We could have used the distributive property first and then solved for R, but notice the multiply by -3 in front of the parenthesis. If we do the opposite operation of multiply by -3, which is divide both sides by -3 first, we save time.

Get ready to try some yourself!

Multiple Choice

3x+1=7

• 2

• $\frac{8}{3}$

• 3

• 8

Multiple Choice

 $\frac{\left(x+2\right)}{2}=4$  Solve for x

• 6

• 0

• 2

• 4