10. A phone plan costs $25/month plus $0.10 per text. Another plan
costs $35/month with unlimited texts. Write an inequality to find
when the first plan is cheaper.
Let t = number of texts. Plan 1: 25 + 0.10t. Plan 2: 35. When is
Plan 1 < Plan 2?
25 + 0.10t < 35 → 0.10t < 10 → t < 100. The
first plan is cheaper when you send fewer than 100 texts.
Real-World Investigations
Investigation 1: Budget Planner
You have $100 to plan a class party. Create a budget using
equations: food costs $f, decorations cost $d, drinks cost $k.
Write an equation where f + d + k = 100. If decorations cost twice
as much as drinks (d = 2k) and food costs $40, find the exact
budget for each category. Then write an inequality showing how the
budget changes if you get a $20 donation.
Materials: calculator, paper for organizing work
Investigation 2: Sports Statistics Analyst
A basketball player scores an average of p points per game. After
8 games, she has 152 total points. Write an equation to find her
average. Then: if she needs at least 200 points in 10 games to
qualify for the all-star team, write an inequality for the minimum
points she needs in the last 2 games. Graph the solution on a
number line.
Materials: number line template, colored pencils
Investigation 3: Temperature Converter
The formula to convert Celsius to Fahrenheit is F = 1.8C + 32. Use
this equation to: (a) Find what 25°C is in Fahrenheit. (b)
Find what temperature in Celsius equals 100°F. (c) Write an
inequality for Celsius temperatures where the Fahrenheit
equivalent is above freezing (F > 32). What does this tell you
about real life?
Materials: calculator, thermometer (optional)
Brain Teasers
Teaser 1: The Mystery Numbers
I am thinking of two numbers. Their sum is 20 and their difference
is 4. Can you write TWO equations and find both numbers?
x + y = 20 and x − y = 4. Adding both: 2x = 24, so x = 12, y
= 8.
Teaser 2: The Balance Scale
On one side of a balance scale, you have 3 identical boxes and a
2-pound weight. On the other side, you have 17 pounds. How much
does each box weigh? Write and solve the equation.
3b + 2 = 17 → 3b = 15 → b = 5 pounds each.
Teaser 3: The Inequality Riddle
I am a whole number. I am greater than 10. I am less than 20. When
you divide me by 3, the answer is a whole number. When you
subtract 6, the result is odd. What numbers could I be?
Divisible by 3 between 10 and 20: {12, 15, 18}. Subtract 6: {6, 9,
12}. Odd results: 9 and 12 are candidates, but 9 is odd (from 15)
→ 15. Also 12 gives 6 (even), 18 gives 12 (even). Only
answer: 15.
Teaser 4: The Parking Puzzle
A parking lot charges $4 to enter and $2 for each hour. Jamie paid
less than $16. Write an inequality. What is the maximum number of
FULL hours Jamie could have parked?
4 + 2h < 16 → 2h < 12 → h < 6. Maximum full
hours = 5.
Where This Math Leads — 7th Grade Preview
Two-Step & Multi-Step Equations
In 7th grade, you will solve equations like 3x + 5 = 20 and 2(x
− 4) = 10 regularly. The one-step skills you learned here
are the building blocks!
Inequalities with Negative Numbers
You will learn that multiplying or dividing an inequality by a
negative number FLIPS the inequality sign. For example, −2x
> 6 becomes x < −3.
Systems of Equations
By 8th grade, you will solve TWO equations with TWO variables at
the same time. The mystery numbers brain teaser above is a taste
of this!
Self-Assessment Checklist
Click each box to track your understanding:
I can determine if a value is a solution to an equation
I can solve one-step addition and subtraction equations
I can solve one-step multiplication and division equations
I can write equations from word problems
I can write inequalities using >, <, ≥, ≤
I can graph inequalities on a number line (open vs. closed
circles)
I understand that inequalities have many solutions
I can solve two-step equations (challenge level)
I can create real-world problems using equations and inequalities