1-1 Intro to solving

1-1 Intro to solving

Solving Techniques

• a solution looks like this x= the letter by itself

• We get the letter by itself by removing other items (numbers or other letters) from the side of the equation that has our chosen letter.

• whatever we do to 1 side of the equal sign, we must do EXACTLY the same thing to the other side.

• lets see what that looks like on the next slide

solving simple equations

• for x-3=10, x is what I want to know the value of. I want x=. I need to get rid of the minus 3 so x will be by itself .

• I will use OPPOSITE OPERATIONS to remove the minus 3 from the left side so x will be by itself (x= ).

• The opposite of minus 3 is plus 3. I will add 3 to both sides of the equal sign

• x-3+3 = 10+3 By adding 3 to both sides I get x by itself since -3 and +3 cancel each other out (opposite operations cancel out)

• Since i added 3 to both sides of the equal sign, I did not change the relationship in the equation. So x =7

• 7+3=10

Multiple Choice

You try:

 $x-6=10$  

• 4

• 10

• 6

• 16

Whats the opposite of multiply?

• Lets try 3 times x = 12

• our answer looks like x = so we need to get x by itself

• We have 3 multiplied to x

• The opposite operation is division so we will divide both sides of the equation by 3

•  $\frac{3x}{3}=\frac{12}{3}$  I divided by 3  on both sides of the equal sign

• The opposite operation worked because  $\frac{3}{3}=1\ \ so\ we\ get\ 1x=4\ \ \ 1x\ is\ the\ same\ thing\ as\ x$  

Multiple Choice

YOU TRY:

 $4x=16$  

• x=12

• x=8

• x=-8

• x=4

what about a more complicated problem

4x-3=21

• Our goal is the same, What does x=. We want x by itself.

• we have -3 and 4times to remove from x.

• Always start with add/subtract to avoid nasty fractions

• 4x-3+3=21+3 We added 3 to both sides to remove the -3 from the side with x. This leaves us with 4x=24

• Now we have 4 times x to remove so we will use OPPOSITE OPERATIONS and divide by the 4 on both sides of the equal sign.

•  $\frac{4x}{4}=\frac{24}{4}\ \ \ \ \ \ \ \ \ x=6$  

Multiple Choice

YOU TRY:

2x+1=13

• x=10

• x=7

• x=6

• x=-6

Poll

How do you feel about solving so far?

• EASY PEASY

• I think I got it

• 50/50

• I definitely need more help

Multiple Choice

-2 + r = 20

• 18
• 22
• -10
• 10

Multiple Choice

18 + n = 31

• 13
• 49

Multiple Choice

a - 10 = 6

• 4
• -4
• 16
• -16

Multiple Choice

Solve for k:
3k + 5 = 23

• k = 4
• k = 5
• k = 6
• k = 7

Multiple Choice

The steps in solving 5b - 6 = 24 are: 

• Add 6 to both sides and divide both sides by 5
• Add 6 to both sides and multiply both sides by 5
• Subtract 6 from both sides then multiply both sides by 5
• Subtract 6 from both sides then divide both sides by 5

Multiple Choice

Solve  3x - 7 = 32

• 13
• -13
• 12
• -12

Multiple Choice

Solve 2x - 3 = 1 

• 3
• 2
• 1
• -2

Multiple Choice

144=12z

• z=20
• z=11
• z=12

Multiple Choice

Which equation has x = 5 as the solution?

• x + 15 = 10
• 2x = 5
• 2x = 10

Multiple Choice

5.    6b = 30

• x = 36
• x = 24
• x = 180
• x = 5

Multiple Choice

x - 62 = 123
How should you show your work to isolate the variable and solve the equation?

• Add 62 to each side. 
• Subtract 62 from each side.
• Multiply each side by 62.
• Add 123 to each side.

Multiple Choice

The solution to the equation makes the equation ______.

• a variable
• an expression
• true
• false

Multiple Choice

What operation would you use to get "x" by itself?
2x = 10

• addition
• subtraction
• multiplication
• division

Multiple Choice

In the equation
4p = 20
 the variable, p, is being multiplied by 4. How should you show your work to isolate the variable and solve the equation?

• Multiply both sides by 4.
  The solution is x = 80.
• Subtract 4 from both sides. 
  The solution is p = 16.
• Add 4 to both sides. The solution is p = 24.
• Divide both sides by 4. The solution is p = 5.

Multiple Choice

The steps in solving 5b - 6 = 24 are: 

• Add 6 to both sides and divide both sides by 5
• Add 6 to both sides and multiply both sides by 5
• Subtract 6 from both sides then multiply both sides by 5
• Subtract 6 from both sides then divide both sides by 5

Multiple Choice

The goal of solving two-step equations is to:

• Move the constant
• Find the coefficient 
• Find the value of the variable
• Combine like terms