Pre-Algebra Chapter 4: Solving Equations

Study Notes

Equations

Equations express equality between two mathematical expressions using the equal sign (=).

One-step Equations

These equations require only one operation to solve for the variable.

Two-step Equations

Involves two operations to find the value of the variable.

Multi-step Equations

Requires multiple operations to solve, utilizing algebraic rules for simplification.

Formulas and Literal Equations

Formulas can involve various variables; solving for a different variable is called solving literal equations. For example, the perimeter P of a square can be rearranged to find the side length s from the formula P = 4s.

Examples for One-step Equations

Example: For x - 6 = -14, adding 6 gives x = -8.
Example: For -3y = 30, dividing by -3 results in y = -10.

Examples for Two-step Equations

Simplifying 2/5m + 3 = 2 by subtracting 3 yields 2/5m = -1, leading to m = -5/2 after proper multiplication.

Steps for Solving Multi-step Equations

Start by distributing and combining like terms.
Move all variable terms to the left side and numerical values to the right side.
Solve the resulting one-step equation.

Examples for Multi-step Equations

For -3(x - 6) + 4(x + 1) = 7x - 10, simplifying leads to combining like terms and solving for x.
Example: x + 22 = 7x - 10 results in -6x = -32 and simplifies to x = 16/3.

Description

Test your knowledge on solving equations with this flashcard quiz for Pre-Algebra Chapter 4. Learn key definitions including one-step and two-step equations, and deepen your understanding of how to manipulate mathematical expressions. Perfect for students looking to reinforce their skills in basic algebra.