Solving Linear Equations and Inequalities

for a number $x$, the distance from $x$ to zero on a number line, represented by $|x|$. If $x\geq 0$, then $\lvert x\rvert=x$. If $x \lt 0$, then $\lvert -x\rvert=x$.

equation that contains an absolute value expression

inequality that contains an absolute value expression

property stating that the solution of an equation does not change after adding the same number to both sides of the equation

property stating that the solution of an inequality does not change after adding the same number to both sides of the inequality

property stating that multiplying an expression by a sum is the same as multiplying the expression by each term in the sum and then adding the products:

property stating that the solution of an equation does not change after dividing both sides of the equation by the same nonzero number

property stating that the solution of an inequality does not change if both sides of the inequality are divided by the same positive number or if both sides of the inequality are divided by the same negative number and the inequality sign is reversed

equation in which each term can be written as a number or a product of the variable and a number. The variable is not raised to a power, in the denominator of a fraction, or under a radical, such as a square root.

inequality in which each term can be written as a number or a product of the variable and a number. The variable is not raised to a power, in the denominator of a fraction, or under a radical such as a square root.

property stating that the solution of an equation does not change after multiplying both sides of the equation by the same nonzero number

property stating that the solution of an inequality does not change if both sides of the inequality are multiplied by the same positive number or if both sides of the inequality are multiplied by the same negative number and the inequality sign is reversed

value of the variable that makes the equation true, which means both sides are equal

value of the variable that makes the inequality true, which means the comparison is valid

property stating that the solution of an equation does not change after subtracting the same number from both sides of the equation

property stating that the solution of an inequality does not change after subtracting the same number from both sides of the inequality