When do you flip inequality signs?

Why do you flip the inequality sign?

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! This is why you must flip the sign whenever you multiply by a negative number.

What are the rules of inequalities?

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.

Do you flip the inequality sign when you square root?

Since square roots are non-negative, inequality (2) is only meaningful if both sides are non-negative. Hence, squaring both sides was indeed valid. Hence, squaring inequalities involving negative numbers will reverse the inequality. For example −3 > −4 but 9 < 16.

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Do you switch the inequality sign when you subtract?

Subtracting the same number from each side of an inequality does not change the direction of the inequality symbol.

What are the four inequality symbols?

The 4 Inequalities

Symbol Words Example
> greater than x+3 > 2
< less than 7x < 28
greater than or equal to 5 ≥ x−1
less than or equal to 2y+1 7

What is the first step to solving an inequality?

To solve an inequality use the following steps:

  1. Step 1 Eliminate fractions by multiplying all terms by the least common denominator of all fractions.
  2. Step 2 Simplify by combining like terms on each side of the inequality.
  3. Step 3 Add or subtract quantities to obtain the unknown on one side and the numbers on the other.

How do you simplify an inequality?

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.

What are some real life examples of inequalities?

Situation Mathematical Inequality
Speed limit Legal speed on the highway ≤ 65 miles per hour
Credit card Monthly payment ≥ 10% of your balance in that billing cycle
Text messaging Allowable number of text messages per month ≤ 250
Travel time Time needed to walk from home to school ≥ 18 minutes

How do you solve absolute value inequalities?

Here are the steps to follow when solving absolute value inequalities:

  1. Isolate the absolute value expression on the left side of the inequality.
  2. 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.
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How do you switch signs in inequalities?

The main situation where you’ll need to flip the inequality sign is when you multiply or divide both sides of an inequality by a negative number. To solve, you need to get all the x-es on the same side of the inequality.

How do you know if inequality is AND or OR?

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).

When graphing do you use an open or closed circle for?

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”. The solution set for this problem will be all values that satisfy both -3 < x and x < 4.

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