Lesson Plan 0 - Quia



Algebra 1 Lesson Notes 1.4 Date ________________

Objective: Translate verbal sentences into equations and inequalities.

equation: a mathematical sentence formed by placing an equal sign, = , between two

expressions.

e.g. 4(6 – 1) = 20

inequality: a mathematical sentence formed by placing one of the inequality symbols,

< , ≤ , > , or ≥ , between two expressions.

e.g. 2(25) > 3(15)

open sentence: an equation or inequality than contains an algebraic expression.

e.g. 2(25) > 3(15) 10m < 36

Mathematical symbols

Symbol Meaning Associated Words

= is equal to, equals is, is the same as

< is less than fewer than

≤ is less than or equal to at most, no more than

> is greater than more than

≥ is greater than or equal to at least, no more than

Practice reading inequalities. READ FROM THE VARIABLE!

e.g. x < 25

−10 ≥ m

6 ≤ b ≤ 8.75

−2 > m > 4

To pick the inequality symbol, ask yourself:

1st: Can it be equal to the value? If yes, be sure to include the = part of the symbol.

2nd: Can it be less than the value? If yes, then use the < symbol. If no, then it must

be greater so use the > symbol.

or

Can it be more than the value? If yes, then use the > symbol. If no, then it must

be less so use the < symbol.

Example 1 (p 21): Write equations and inequalities

Verbal sentence Expression

a. the sum of twice a number r and 3 is more than 11 2r + 3 > 11

b. the quotient of a number n and 2 is at most 16 [pic] ≤ 16

d. the product of 5 and the difference of a and b is 24 5(a – b) = 24

c. a number q is at least 5 and less than 17 5 ≤ q < 17

why not 5 ≥ q < 17 ?

solution of an equation / solution of an inequality: a number that makes the equation or

inequality true .

When you substitute a number for a variable in an open sentence and the resulting statement is true, then the number is a solution of the equation or inequality.

Example 2 (p 22): Check possible solutions

Check whether 5 is a solution of the equation or inequality.

a. 24 – 3d = 9 9 = 9 (

b. 3x + 4 = 18 19 ( 18

c. 2w – 7 ≤ 4 3 ≤ 4 (

d. 4 + 3p > 19 19 19

Example 4 (p 23): Solve a multi-step problem

Sarah enrolled in a guitar class. The enrollment fee was $25. She paid a total of $70

for the enrollment fee and 3 lessons.

What is the cost of 3 lessons?

How much did each lesson cost?

Write an equation to model the situation.

Example 5 (p 23): Write and check a solution of an inequality

Write an inequality to model the situation. Then evaluate to solve the problem.

a. Tyler would like to make no less than $610 selling coffee mugs online. He sells the

mugs for $22 each. If he sells 28 mugs, will be achieve his goal?

b. Sadie was hoping to make at least $250 profit on items she made and sold at a craft fair

one weekend. Her cost for materials needed to make the merchandise was $210.

If she sold $340 of merchandise on Saturday and $180 on Sunday, did she sell enough

merchandise to meet her goal?

Hint: How would she calculate her profit?

( HW: A6a pp 24-26 #2-28 even, 36, 40-46 even

A6b pp 24-26 #3-27 odd, 35, 39-45 odd

Prepare for Quiz 1.3-1.4

( HW: A6c Lesson 1.4 Practice B

( CW/HW: A6d p 27 Mixed Review 1.1-1.4 #1-7

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