Question

module 3 topic 1 lesson 2 & 3 dol
student outcomes:
lo: i will write and solve inequalities, analyze a graph on a coordinate plane to solve
problems involving inequalities, and interpret how a negative rate affects how to solve an
inequality. i will recognize and use literal equations. i will rearrange literal equations to
highlight quantities of interest. (a.2c, a.5b, a.12e)
dol: i will solve literal equations and use inequalities successfully in at least 4 to 5 questions.
name: _ date: _

1. michael earns $16 per hour for working at his job. this week, he also receives

a bonus of $500. how many hours does he need to work to earn at least $900
this week?
which inequality represents the situation?
a. 16h + 500 > 900
b 16h + 500 ≥ 900
c. 500h - 16 ≥ 900
d. 16h - 500 ≥ 900

1. clara spends $90 on supplies to make bracelets. she sells each bracelet she

makes for $8. how many bracelets must she sell to earn a profit?
she needs to sell at least ___ bracelets.

1. the formula for the area of a triangle is a = \\( \frac { 1 } { 2 } b h \\).

solve for b.
a. b = \\( \frac { 2 a } { h } \\)
b. b = 2a - h
c. b = ah - 2
d b = 2ah

Explanation:

1.

Step1: Analyze Michael's earnings

Michael earns $16 per hour (so total earnings from hours worked is LXI0) and has a $500 bonus. He needs to earn at least $900. The phrase "at least" means \(\geq\).
The inequality is \(16h + 500\geq900\).

2.

Step1: Set up the profit - cost equation

Let \(x\) be the number of bracelets. Cost is $90 and revenue is \(8x\). To make a profit, \(8x>90\).

Step2: Solve the inequality

Divide both sides of \(8x > 90\) by 8: \(x>\frac{90}{8}=11.25\). Since the number of bracelets must be a whole number, \(x = 12\).

3.

Step1: Solve the area formula for \(b\)

Given \(A=\frac{1}{2}bh\). Multiply both sides by 2 to get \(2A=bh\).

Step2: Isolate \(b\)

Divide both sides of \(2A = bh\) by \(h\) (assuming \(h
eq0\)): \(b=\frac{2A}{h}\).

Answer:

1. B. \(16h + 500\geq900\)
2. \(12\)
3. A. \(b = \frac{2A}{h}\)