Summary Algebra 1 / Algebra I – Revision Pack – Introductory Algebra Course – Comprehensive Study Notes and Practice Questions

Algebra 1 / Algebra I – Revision Pack –
Introductory Algebra Course –
Comprehensive Study Notes and Practice
Questions
Equations & Inequalities (Exam-Focused Notes)


📘 1. Linear Equations
A linear equation is in the form:
ax + b = 0

Steps to Solve:

1. Simplify both sides
2. Move variables to one side
3. Move constants to the other side
4. Divide to isolate the variable

Worked Example:

Solve: 2x + 5 = 13
2x = 8
x=4

Shortcut:

Move across = change sign




📘 2. Equations with Brackets (Distributive Property)
Worked Example:

Solve: 3(x + 2) = 12
3x + 6 = 12

, 3x = 6
x=2

Shortcut:

Always distribute (multiply) across the parentheses first




📘 3. Equations with Fractions
Worked Example:

Solve: x/2 + 3 = 7
Multiply by 2:
x + 6 = 14
x=8

Shortcut:

Multiply by the least common denominator (LCD) to remove fractions




📘 4. Inequalities
Examples of inequality signs:

greater than
< less than
≥ greater than or equal to
≤ less than or equal to

Worked Example:

Solve: 2x + 3 > 7
2x > 4
x>2

IMPORTANT RULE:

If you multiply or divide by a negative number, flip the inequality sign.

Example: