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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