Algebra 2 Honors
Do Now
Name: ________________________
Oh yeah, huh… (Error Correction!)
Directions: For each problem, determine if the answer is correct. If it is not, explain what the
mistake is and correct it.
Write the numbers that are represented in both inequality and interval notation:
1)
Inequality Notation: x < 2
Interval Notation: ( -¥,2 ]
Explanation of problem:
2)
Inequality Notation: x > -1 or x > 1.5
Interval Notation:
Explanation of problem:
3)
Inequality Notation: -1 < x £ -5
Interval Notation: [ -5,-1)
Explanation of problem:
4)
Inequality Notation: -3 < x < -1 or x > 0
Interval Notation:
Explanation of problem:
5)
Inequality Notation: x < -3 or x > 3
Explanation of problem:
Interval Notation:
Solve the following equations:
6)
3
( 2x + 1) - 6 = 5
4
æ3
ö
a) 4 ç ( 2x + 1) - 6 = 5 ÷
è4
ø
b) 3(8x + 4) - 24 = 20
c) 24 x + 12 - 24 = 20
d) 24 x - 12 = 20
e) 24 x = 32
32
f) x =
24
7) 2x + 5 - 3 = 7
a) 2x + 5 - 3 = -7 or
b) 2x + 2 = -7
2x + 5 - 3 = 7
2x + 2 = 10
c) 2x = -9
2x = 8
d) x = -4
1
2
or
x=4
Algebra 2 Honors
Pair Work
Name: _____________________
Solving Absolute Value Inequalities
Solve each equation and graph the solution. Make sure to follow the 5-step model outlined in
your notes.
Hint: one of these has no solution – can you figure out which one and why?
1)
x-7 £5
2)
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
3)
4 - 3x ³ 5
4)
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
2x + 1 > 5
1-
2
x < 10
3
5)
2 3x - 1 - 6 £ -2
6)
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
7)
2
1
- 5x + 10 = 36
2
8)
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
1
3x - 4 + 6 < 3
2
1 1 1
- x - 3>2
5 3 2
Algebra 2 Honors
Homework #1-12
Name: _____________________
Absolute Value Inequalities
1) Convert each decimal to a fraction.
a. 4.057
b. 0.27
c. 0.5582
2) Show the full process to answer the word problem: define the variables, write the system of
equations, solve the system, write the answer in a sentence.
A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4
trees, and totaled $487. The second order was for 6 bushes and 2 trees, and totaled $232. The bill
did not list the price of the bushes and the trees separately. How much would it cost to order 2
bushes and 5 trees from the same nursery?
Solve each absolute value problem and graph the solution on a number line. Make sure to
show all 5 steps clearly. If there is no solution, explain why.
Pay attention:
 first check if it is an equation, a “less than” inequality, or a “greater than” inequality.
 remember to change the direction of the inequality (when necessary).
3) 2x - 5 - 7 = 3
4) 4x - 2 + 1 > 9
5) 2 x + 5 £ 11
6)
7
x + 13 + 7 < 6
9
7) 2 5 - 4x - 3 ³ 15
8)
5 1
- x -2<6
3 4
9) Go back and write the solution to problems 4 – 8 in interval notation also.
Challenge (If you can solve this inequality correctly, you’re on fire! You might even get some
bonus homework points if you can explain your work.)
-
5
4
6 - x + 2 > 12
7
5