Sue picked apples from Farmer Brown's trees. She was allowed to pick up to 20 apples. After an hour, Bob asked Sue how many apples she had picked. Sue said she did not yet reach her limit, but if she had twice as many as she currently has plus half as many as she currently has, she would have reached her limit. The summary asks how many apples Sue has picked.

1. Today:

2. Warm-Up
3. (
𝒈
𝟑
) + (
𝟐
𝟓
) = (
𝟑
𝟐
) - g
1. 2.
4.
Farmer Brown let Sue pick apples from his trees for free, but
her limit was 20.. After an hour, Bob asked Sue if she reached
her limit. Sue replied, "Not yet. But if I had twice as many as I
have now, plus half as many as I have now, I would have my
limit." How many apples has Sue picked?
Find two consecutive even integers where twice the
larger is forty less than three times the smaller.

3. Simplify:
( + ) + ( - ) +
= + + - +
Combine Like Terms: = 2 +
Distribute:
Algebra: Its not about the numbers!

4. WARM-UPTranslating

5. Writing & Interpreting Decimals:

6. Solving Equations with Variables on Both Sides
 When an equation has variables on both sides,
three different results are possible.
 Write & solve this equation: 2x + 2 = 4 + x
The equation results in a solution of a single number.
In this case, x = 2
1. Most of the equations we solve are conditional equations

7. A 2nd
Possibility
 3x - 9 = 3x + 10
 A linear equation has NO SOLUTION when the solved
equation has no variable and the equation is false.
3x - 3x = no variable, -9 = 10

8. A 3rd
Possibility
 When an equation has variables on both sides ,something
else may occur. Solve the equation: 4(x – 5) = 4x - 20
4x -20 = 4x -20; Subtract 4x from the left side and -20 = -20
These are called identity equations. It means ALL
REAL NUMBERS make the sentence true.
A linear equation is an identity when the solved equation
has NO VARIABLE and the solution is TRUE!
In other words, no matter what number we substitute for
x, the equation will be true.
2. When solving these types of problems, write Infinite
Solutions on your paper.

9. Therefore…
• When solving equations with variables on both
sides, 3 different things can happen.
1) solution is a single number (x = 4) (conditional)
2) solution is NO SOLUTION (Contradiction)
3) solution is ALL REAL Numbers ( IDENTITY)

10. Class Work 1.4
Please copy the problems. This classwork is due at the
beginning of class Thursday, October 22.
Make a note in your grade tracker. (Along with the Khan
Academy topics due Wednesday.
CW 1.4