Transcript Unit 1 – Foundations of Algebra

Unit 2 – Linear Equations & Inequalities
Topic: Solving Linear Equations, Inequalities, &
Proportions (This PowerPoint contains homework
problems which are due next week)
Reminders from Algebra 1
 Identity
 A statement that is always true
 Ex. 4x – 6 = 2(2x – 3)
 Contradiction
 A statement that is never true
 Ex. 3a + 4 < 3a
 Properties of equality
 Whatever you do to one side of an
equation or inequality, you must do to
the other side
Reminders from Algebra 1
 Solutions to an inequality must be
graphed on a number line
 Ex. 4x – 18 ≥ 2x + 6
2 x  24
x  12
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Homework Problems
 The following slides contain your
homework problems. On your own
paper, write the problems and work out
your solutions. Alternatively, you may
print the slides as handouts (3 per page)
and work the problems on the lines next
to each slide. Due Wednesday, 8/17 (Aday) or Thursday, 8/18 (B-day). Come
with questions next class.
Homework Problems
1. What value(s) of k make the equation
2(x – k) = 2x – 20 an identity?
2. Karla wants to spend less than $50 at the grocery
store. She already has $37 worth of groceries in her
cart and is going to buy some fresh veggies for
$0.75 each. Write & solve an inequality to
determine the numbers of veggies she can buy and
stay under her spending limit?
Homework Problems
3. In 2004, three receivers for the Indianapolis Colts
caught a total of 37 touchdowns. Reggie Wayne
caught 2 more than Brandon Stokely, and Marvin
Harrison caught 3 more than Reggie Wayne. How
many touchdowns did each receiver catch?
Homework Problems
4. Find the measure of each angle in the triangle
below.
B
2xº
A
xº
(x – 20)º
C
Homework Problems
5. A basketball rim 10 ft. high casts a shadow 15 ft.
long. At the same time, a nearby building casts a
shadow that is 54 ft. long. How tall is the
building?
Homework Problems
6. Sandy wants to measure the distance across a
stream. She took some measurements and drew the
diagram below. How wide is the stream?
Homework Problems
Solve each of the following. If necessary, graph the
solutions.
5
4

7. 3( x  1)  7( x  3) 9.
v6
12
3t 

8. 7t  6  2 5    5t  11 10. 5( x  2)  4(2 x  6)  2
2

Homework Problems (10 pt. Extra
Credit)
a c

b d
d b
 ,
c a
 Given
, prove algebraically that
assuming
that none of the variables equal 0. Your proof must be
complete in order to earn the extra credit, but may be in
any format you wish.