Key Concepts

• The addition and multiplication properties of equality allow the same operation to be performed on both sides of an equation
• To solve an equation containing an absolute value, first isolate the absolute value then write two equations: [latex]|u| = c[/latex] and [latex]|u| = -c[/latex]
• Use the distributive property to eliminate parentheses in equations before collecting and combining like terms.
• Use the multiplication property of equality to eliminate fractions from equations by multiplying both sides by the LCD.
• Eliminate decimals from an equation by multiplying both sides by a sufficient factor of 10.
• Equations may have one unique solution, no solutions, or an infinite number of solutions.

Glossary

coefficient a number multiplying a variable

conditional equation an equation that has a finite number of solutions

equation a mathematical statement of equivalency between two expressions

expression groups of terms connected by addition or subtraction

identity an equation that has infinitely many solutions

inconsistent equation an equation that has no solution

term a single number, or variables and numbers connected by multiplication

variable a symbol that stands for an unknown quantity, often represented by letters such as [latex]x, y,[/latex] or [latex]z[/latex].