Section 2.4Now You Can Solve Problems instead of just creating them!

Intro to Equations

Equation Can be Numerical or Variable Has an equals sign or >, <.

9+3=12 3x-2=10

True or False

A true equationx+8=13

If x = 5 then5+8= 13 Note: this is true

True or False

False Equation If 9+2y = 49

So if we substitute 6 in for y Then 9+2*6 = 49 This is a lie!

Solutions

A solution to an equation is a number that make the equation true.

For example: Is 2 a solution of 2x-5=x2-3 Lets find out by subbing in -2 2*(2)-5 = (2)2-3 4-5 = 4-3 -1 = 1

More examples

Is -4 a sol’n of 5x-2=6x+2

5x-2=6x+2 5(-4)-2 = 6(-4)+2 -20 -2 = -24 + 2 -22= -22

YES!

Even more examples

Is -4 a sol’n of 4+5x = x2-2x

4+5x = x2-2x 4+5(-4)=(-4)2-2(-4)

4+(-20)=16-(-8) -16=24

NO!

Give it a try Is (4) a solution to 5-4x=8x+2?

Is 5 a solution of 10x-x2=3x-10

Is -6 a solution of 4x+3=2x-9 Yes Is (-3) a solution of 4-6x=9x+1 No Is -5 a solution of x2=25 Yes’m

Opposites

Remember: solving algebraic equations is all about opposites.

i.e. do the opposite of the whatever the mathematical operation is.

Solving Stuff What you want at the end of all your

work The variable to = a constant Like y=5

What's the opposite of: Addition Subtraction Multiplication Division Exponents Square Roots

Square Roots

Break it down Examples:

Square roots of 49, 18, 27

You try: Square roots of

44, 96, 45

Back to where we were

First form X+a=b

X+3=5 Try to get simplify first (PEMDAS) Try to isolate the variable Do the opposite X+3 =5 -3 -3 X =2

Example

Y+3=2 -3 -3 Y = -1

Check your answer Sub in what you found for Y into the

original equation

Things are what they appear?

3=T+5 It’s the same thing– get everything

away from the variable. 3=T+ 5 -5 -5 -2 =T Check your answer

Try These

5 = x + 5 x=0

X-(4) = 6 X= 10

The second type Form ax=b 2x=6 What’s the operation between the 2 and

the x? What's the opposite? Do it! 2x=6 2 2 x=3

You try it -2x = 6 -3

8x = 16 2

64 = 16x 4

2z = 0 0

Applications and Formulas

Turning words into equations

The many words for “=“

Equals, is equal to, is, represents, was, is the same as

Processsssss

1. Give the unknown a letter 2. Break the problem down at the

“=“ 3. Translate as you read 4. The “and”

Examples Negative fifty-six equals negative eight

times a number. Find the number. The high temperature today is 7 degrees

lower than the high temperature yesterday. The high temperature today is -13. What was the high temperature yesterday?

A jeweler wants to make a profit of 250 on the sale of a bracelet that cost 700. Use

P = S – C where p is the profit, s is the selling price, and c is the cost to find s.

You try it now The temperature now is 8 degrees lower than

yesterday. The temperature is -16 now. What was the temperature yesterday?

In the US, the average income of people 25 to 34 is $14886 less than people 45 to 54. The average income of people 24 to 34 is 41,414. Find the income of the 45 to 54 year olds.

The velocity (same as speed) of a falling object is given by the formula v=gt2 where v is velocity, g is gravity at 9.8 and t is time. What’s the velocity of a rock falling for 3 seconds?

2.4 a Homework

1 thru 47 eoo 2, 10, 16, 26, 28, 32, 38, 42, 46, 50