ALGEBRA 1: CORE BASICS STUDY GUIDE
Published by Math Notes — Premium Step-by-Step Study Summaries
Welcome to your ultimate Algebra 1 quick-reference guide! This summary breaks down the most essential concepts
needed to master basic equations, inequalities, and linear graphing. Use this layout to study for midterms, finals, or
daily homework.
1. Solving Multi-Step Equations
To solve for an unknown variable (like x), you must isolate it on one side of the equals sign by using Inverse
Operations (doing the exact opposite action).
Step Order Operation Rule Example: Solve 2x + 5 = 11
1. Simplify Clear parentheses using distributive property & 2x + 5 = 11 (Already simplified)
combine like terms.
2. Undo + / - Subtract or add constants to move them away Subtract 5 from both sides:
from the variable. 2x = 11 - 5 -> 2x = 6
3. Undo * / ÷ Multiply or divide to fully isolate your target Divide both sides by 2:
variable. x = -> x = 3
2. Graphing Linear Equations (y = mx + b)
Any straight line on a coordinate plane can be written using Slope-Intercept Form:
• y = mx + b
• m = the Slope of the line (Rise over Run). Tells you how steep the line is.
• b = the y-intercept. This is the exact point where the line crosses the vertical y-axis (0, b).
Slope Direction Visual Behavior Formula to Calculate (m)
(y&sub2; - y&sub1;)
Positive Slope (m > 0) Line goes UP from left to right. /
(x&sub2; - x&sub1;)
Negative Slope (m < 0) Line goes DOWN from left to right. Rise / Run
Zero Slope (m = 0) Perfectly flat, Horizontal line. Horizontal Line: y = b
3. Golden Rules of Inequalities
Inequalities use signs like < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).
They follow the exact same rules as normal equations, with one major exception:
CRITICAL PUBLISHER TIP: Whenever you multiply or divide both sides of an inequality by a NEGATIVE
NUMBER, you must FLIP the inequality sign in the opposite direction! (e.g., -2x < 6 becomes x > -3).
Published by Math Notes — Premium Step-by-Step Study Summaries
Welcome to your ultimate Algebra 1 quick-reference guide! This summary breaks down the most essential concepts
needed to master basic equations, inequalities, and linear graphing. Use this layout to study for midterms, finals, or
daily homework.
1. Solving Multi-Step Equations
To solve for an unknown variable (like x), you must isolate it on one side of the equals sign by using Inverse
Operations (doing the exact opposite action).
Step Order Operation Rule Example: Solve 2x + 5 = 11
1. Simplify Clear parentheses using distributive property & 2x + 5 = 11 (Already simplified)
combine like terms.
2. Undo + / - Subtract or add constants to move them away Subtract 5 from both sides:
from the variable. 2x = 11 - 5 -> 2x = 6
3. Undo * / ÷ Multiply or divide to fully isolate your target Divide both sides by 2:
variable. x = -> x = 3
2. Graphing Linear Equations (y = mx + b)
Any straight line on a coordinate plane can be written using Slope-Intercept Form:
• y = mx + b
• m = the Slope of the line (Rise over Run). Tells you how steep the line is.
• b = the y-intercept. This is the exact point where the line crosses the vertical y-axis (0, b).
Slope Direction Visual Behavior Formula to Calculate (m)
(y&sub2; - y&sub1;)
Positive Slope (m > 0) Line goes UP from left to right. /
(x&sub2; - x&sub1;)
Negative Slope (m < 0) Line goes DOWN from left to right. Rise / Run
Zero Slope (m = 0) Perfectly flat, Horizontal line. Horizontal Line: y = b
3. Golden Rules of Inequalities
Inequalities use signs like < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).
They follow the exact same rules as normal equations, with one major exception:
CRITICAL PUBLISHER TIP: Whenever you multiply or divide both sides of an inequality by a NEGATIVE
NUMBER, you must FLIP the inequality sign in the opposite direction! (e.g., -2x < 6 becomes x > -3).
