Section 2.4 Now 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 equation x+8=13 If x = 5 then 5+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=x 2 -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  =  -22= -22  YES!

Even more examples  Is -4 a sol’n of 4+5x = x 2 -2x  4+5x = x 2 -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-x 2 =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 x 2 =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 =  X =2

Example  Y+3=2   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   -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2  64 = 16x 44  2z = 0 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=gt 2 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