An algebraic equation is a mathematical relationship involving one or more variables. In an algebraic equation, the goal is to find the value(s) of variables that make the equation true.
For a mathematical statement to be considered an algebraic equation, it needs two components: one or more variables and an equal sign.
|10x+6=36| is an algebraic equation since a variable and an equal sign are present.
|5+10=15| is not an algebraic equation since there is no variable; it is an arithmetic operation that represents an equality.
|2x-7| is not an equation since there is no equal sign. It is simply an algebraic expression.
|\dfrac{x+7}{x+4}=\dfrac{2x-3}{2x}| is an algebraic equation since it contains both a variable and an equal sign.
|a-12<9| is not an equation since it has an inequality sign. The relationship is one of inequality and not equality. Instead, it is an inequality.
Mathematical equations are not always given directly in a written problem. To solve this kind of situation, first translate the written statements into one or more equations. Then, solve the equation(s) to find the solution(s) to the problem.
Pour valider ta compréhension à propos de la résolution de problèmes algébriques de façon interactive, consulte la MiniRécup suivante :
An algebraic inequality is a mathematical expression involving one or more variables. In an inequality, the goal is to find a set of values (the solution set) that makes the inequality true.
For a mathematical statement to be considered an algebraic inequality, it needs two components: one or more variables, and an inequality relation.
|x>3| is an algebraic inequality since there is a variable and an inequality relation.
|8>3| is not an algebraic inequality since there is no variable.
|2m+6\le15| is an algebraic inequality since there is a variable and an inequality relation.
|2x=14| is not an algebraic inequality since it demonstrates equality and not an inequality.
|3+5=8| is not an algebraic inequality since there is neither a variable nor an inequality relation.
The following are the inequality symbols used in inequalities, and their definitions:
| symbol | definition |
|---|---|
| |<| | "Less than" |
| |\le| | "Less than or equal to" |
| |>| | "Greater than" |
| |\ge| | "Greater than or equal to" |
Unlike an algebraic equation, an algebraic inequality does not have a single solution, but rather a set of values that make the inequality true. The values which satisfy the inequality are called a solution set.