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Dino Algebra 1

20 Essential Problems — All Key Topics · With Rex!

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Hey there, Math Explorer! I'm Rex 🦖 — the world's smartest algebra dinosaur. Tap a topic below to unlock the concept, then crush the quiz! Roar! 🌟
📖 Topics — Tap to Explore
🔢Linear Equations
⚡Inequalities
📈Slope & Lines
🎯Systems
🧩Distributive
🔑Factoring
📐Quadratics
🚀Exponents
📏Absolute Value
🎲Functions

🔢 Linear Equations

🦖 Rex's Rule: Whatever you do to one side, do the same to the other!
Goal: Isolate x
ax + b = c → x = (c − b) / a
Steps:
1. Move constants to one side (+/−)
2. Move coefficients (× / ÷)
3. Simplify
Example
3x + 7 = 22
3x = 22 − 7 = 15
x = 15 ÷ 3
✅ x = 5

⚡ Inequalities

🦖 Key Rule: Multiply or divide by a NEGATIVE? Flip the sign!
ax + b < c, ax + b > c
ax + b ≤ c, ax + b ≥ c
Example
2x − 5 < 9
2x < 14
x < 7
✅ x < 7 (open circle on 7)
Compound Inequality
−3 < 2x+1 ≤ 9
−4 < 2x ≤ 8
−2 < x ≤ 4
✅ −2 < x ≤ 4

📈 Slope & Lines

Slope = (y₂ − y₁) / (x₂ − x₁)

Slope-Intercept: y = mx + b
m = slope, b = y-intercept

Standard: Ax + By = C → y = (−A/B)x + C/B
🦖 Remember: Slope = Rise over Run!
Find slope: (2,3) and (6,11)
m = (11−3)/(6−2) = 8/4
✅ m = 2
4x − 2y = 8 → standard to slope-intercept
−2y = −4x + 8
y = 2x − 4
✅ slope = 2, y-intercept = −4

🎯 Systems of Equations

Method 1: Substitution
Solve one equation for a variable, substitute

Method 2: Elimination
Add/subtract equations to cancel a variable
Elimination: x+y=10, x−y=4
Add: 2x = 14 → x = 7
7 + y = 10 → y = 3
✅ (7, 3)
Substitution: y=2x+1, y=x+4
2x+1 = x+4 → x=3, y=7
✅ (3, 7)

🧩 Distributive Property & Like Terms

a(b + c) = ab + ac

Like terms: same variable + same exponent
4x² + 3x − 2x² + 5x = 2x² + 8x
Example
3(2x − 5) = 6x − 15
✅ 6x − 15
🦖 Only combine terms with the SAME variable and exponent!

🔑 Factoring

x² + bx + c = (x + p)(x + q)
where p + q = b and p × q = c
🦖 Find two numbers that ADD to b and MULTIPLY to c!
x² + 5x + 6
p+q = 5, p×q = 6
→ p=2, q=3
✅ (x + 2)(x + 3)
Zero Product Property
(x−3)(x+5) = 0
x−3=0 or x+5=0
✅ x = 3 or x = −5

📐 Quadratic Equations

ax² + bx + c = 0

Quadratic Formula:
x = [−b ± √(b²−4ac)] / 2a

Discriminant: b²−4ac
> 0: two real roots
= 0: one real root
< 0: no real roots
x² − 5x + 6 = 0
Factor: (x−2)(x−3)=0
✅ x = 2 or x = 3
Discriminant: x²−4x+5
b²−4ac = 16−20 = −4
✅ No real solutions

🚀 Exponent Rules

Product Rule: xᵃ · xᵇ = xᵃ⁺ᵇ
Quotient Rule: xᵃ / xᵇ = xᵃ⁻ᵇ
Power Rule: (xᵃ)ᵇ = xᵃᵇ
Zero Exponent: x⁰ = 1 (x≠0)
Negative Exponent: x⁻ⁿ = 1/xⁿ
Examples
x³ · x⁴ = x⁷
(2x²)³ = 8x⁶
✅ Add exponents when multiplying!

📏 Absolute Value

|x| = distance from zero on number line

|ax + b| = c → ax+b = c OR ax+b = −c
(when c ≥ 0)
🦖 Absolute value always gives a non-negative result!
|2x − 4| = 8
Case 1: 2x−4=8 → x=6
Case 2: 2x−4=−8 → x=−2
✅ x = 6 or x = −2

🎲 Functions & Proportions

Function Notation: f(x) = expression
f(a) = substitute x = a and evaluate

Proportion: a/b = c/d → ad = bc
Percent: Part = Percent × Whole
f(x) = 2x + 3, find f(4)
f(4) = 2(4) + 3 = 8 + 3
✅ f(4) = 11
Proportion: 3/x = 12/20
12x = 60 → x = 5
✅ x = 5