A linear equation is an algebraic equation that represents a straight line when graphed. It is an equation in which the variables are raised to the power of 1 and are not multiplied or divided by each other. The general form of a linear equation in one variable (x) is:
ax + b = 0
where “a” and “b” are constants, and “x” is the variable. The goal of solving a linear equation is to determine the value(s) of the variable that satisfy the equation.
To solve a linear equation, follow these steps.
Simplify the equation if necessary by combining like terms or using the distributive property.
Isolate the variable term (the term with “x”) on one side of the equation by adding or subtracting constants or variable terms to both sides.
If the variable term is multiplied by a coefficient, divide both sides of the equation by that coefficient to isolate the variable.
After isolating the variable, the equation should be in the form “x = constant” or “x = expression.”
Inequalities:
In mathematics, inequalities are statements that compare the relative values of two expressions. They indicate that one quantity is greater than, less than, or equal to another quantity. The most common types of inequalities are:
Greater than (>): It states that one value is larger than another. For example, “x > 5” means that the variable x is greater than 5.
Less than (<): It states that one value is smaller than another. For example, “y < 10” means that the variable y is less than 10.
Greater than or equal to (≥): It states that one value is either greater than or equal to another. For example, “a ≥ 3” means that the variable a is either greater than or equal to 3.
Less than or equal to (≤): It states that one value is either less than or equal to another. For example, “b ≤ 7” means that the variable b is either less than or equal to 7.