Much like when you divide by a negative number, the sign of the inequality must flip! Here’s why: When you multiply both sides by a negative value you make the side that is greater have a “bigger” negative number, which actually means it is now less than the other side!
Subtracting the same number from each side of an inequality does not change the direction of the inequality symbol. If a < b and if c is a positive number, then a · c < b · c. Multiplying each side of an inequality by a positive number does not change the direction of the inequality symbol.
When solving an inequality: • you can add the same quantity to each side • you can subtract the same quantity from each side • you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.
A compound inequality is just more than one inequality that we want to solve at the same time. We can either use the word ‘and’ or ‘or’ to indicate if we are looking at the solution to both inequalities (and), or if we are looking at the solution to either one of the inequalities (or).
These inequality symbols are: less than (<), greater than (>), less than or equal ( ≤ ), greater than or equal (≥) and the not equal symbol (≠). Inequalities are used to make a comparison between numbers and to determine the range or ranges of values that satisfy the conditions of a given variable.
To solve an inequality use the following steps: Step 1 Eliminate fractions by multiplying all terms by the least common denominator of all fractions. Step 2 Simplify by combining like terms on each side of the inequality. Step 3 Add or subtract quantities to obtain the unknown on one side and the numbers on the other.
Flip the inequality sign when you multiply or divide both sides of an inequality by a negative number. You also often need to flip the inequality sign when solving inequalities with absolute values.
Summary. Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the inequality: Multiplying or dividing both sides by a negative number.
You will determine the solution set of an inequality by equating them first into zero. After that try to substitute the value of X. Then after, you will find out the right sign that you will use.
You can find the range of values of x, by solving the inequality as if it was a normal equation. (This means that when the value of x is less than 2, the inequality 4x – 5 < x + 1 is true.)
To graph the solution set of an inequality with two variables, first graph the boundary with a dashed or solid line depending on the inequality. If given a strict inequality, use a dashed line for the boundary. If given an inclusive inequality, use a solid line. Next, choose a test point not on the boundary.
When graphing a linear inequality on a number line, use an open circle for “less than” or “greater than”, and a closed circle for “less than or equal to” or “greater than or equal to”.
Isolate the absolute value expression on the left side of the inequality. If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions.
If the inequality states something untrue there is no solution. If an inequality would be true for all possible values, the answer is all real numbers.