Chapter 3 Unit Question How do we Solve Equations in Algebra?

Open Learning Logs Date on Left…Section 3 – 2 on right

Warm – Up 1.The reciprocal of -8 is ________. 2.The product of zero and any number is ________. 3.The only number without a reciprocal is ________. 4.There are two numbers that equal their own reciprocal. They are ________ and ________.

Section 2 How do we solve and check equations of the form ax = b? How do zero and -1 as values for a and b affect the solution?

Homework Check

Multiplication Property of Equality For all Real numbers m, n, and c … If m = n, then cm = cn This is saying that I can multiply an equality by anything, as long as I multiply BOTH SIDES by the SAME THING

We can expand this to solve equations! Example: 3x = 6 I choose to let c = 1/3 If we assume this is true then from the general form ax = b we can say a = 3 and b = 6. We need to find a value to multiply both sides by to get x all by itself.

Summarizing… So…the trick is coming up with a something to multiply both sides of an equation. To solve ax = b for x, multiply both sides of the equation by the reciprocal of a ! AND THAT TRICK IS…

Again…solve… A different way… Something we’ll call… “Bring down…Bring over” Use with anything that is NOT a fraction Example: 3x = 6

Again…solve…

Why not just use “Bring down…Bring Over” all the time? Examples:

…for Solve…

Solve! 0x = 40x = 0 What can you possibly multiply by zero and get 4? What can you possibly multiply by zero and get 0? NOTHING! We call that “No Solution” EVERYTHING! We call that “All Real Numbers”

SOLVE!

In set notation then… { 0 } The solution is zero 63x = 0 Set of all Real numbers All Real numbers are solutions 0x = 0 { } or ø There is no solution 0x = 4 Solution SetSentenceEquation

Solve! -x = But –x = -1 x does it not? Substitute! We need x NOT –x !!!! -1 x = x = x = Let’s call this the “Gush” property so we can avoid showing this work!

Solve! -a = x = 42 0z = 0423y = y = 0 { } All Real Numbers a = GUSH!

Homework Do HoffmaSheet 3 – 2

Solve… When Dax types essays, he types 250 words per minute. About how many minutes will he need for a 1500 word essay? Let x = # of minutes 250x = 1500 minutes

Solve… Suppose a calculator has 6 keys in a row. How many rows are needed for a 56-key calculator? Let r = # of rows 6r = 56 So, 10 rows

Warm - Up