Chapter 1
Number and Quantity
Course: Core Academic Skills For Educators Combined Test 5752
Subject: Core Academic Skills Educators Mathematics 5733
Chapter: Algebra
A linear equation in one variable is an equation that can be expressed in the form
ax + b = c
where a, b, and c are constants, and a ≠ 0. Solving such equations means finding the value of the variable that makes the equation true. Linear equations in one variable always graph as a straight line on the coordinate plane, but because there is only one variable, the solution is a single numerical value rather than a point on a plane.
General principles
- Linear equations maintain balance. Whatever operation is applied to one side must be applied to the other side.
- The ultimate goal is to isolate the variable on one side of the equation.
- Simplification may be needed before solving: apply distributive property, remove parentheses, and combine like terms.
- Solutions can be unique (one solution), infinite (identity), or nonexistent (contradiction).