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

12

242

x

x

7 8 9 10 11 12 13 14 15 16 17

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 (A-day) 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.

2xº

xº (x – 20)ºA C

B

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

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8.

9.

10.

Solve each of the following. If necessary, graph the solutions.

)3(7)1(3 xx

2)62(4)2(5 xx1152

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4

6

5

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Homework Problems (10 pt. Extra Credit)

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.

d

c

b

a

a

b

c

d