When do you flip inequality signs

Viewed k times. Sniper Clown Sniper Clown 1, 2 2 gold badges 17 17 silver badges 34 34 bronze badges. Instead I give link on Inequalities by Lawrence Spector which answers it in thorough detail introducing theorem of inequalities and their proofs. Add a comment. Active Oldest Votes. Seeing why 1 is true is not too hard.

The other cases can be handled similarly. But, perhaps a bit of rigor is needed here. David Mitra David Mitra Either it is circular or so incomplete to be of little help. Alas, the OP doesn't know what he's missing by accepting it. Perhaps you may wish to do him a favor by improving the answer. However, after reading your answer it appears the short and straight answer is because of law of signs which I think is what I was looking for.

The reason that the reversal for equality escapes notice is that the symbol for equality is symmetric. Dave L. Follow the steps to solve the problem. Step 1: Multiply the entire first equation by 2. Step 2: Rewrite the system of equations, replacing the first equation with the new equation. Step 3: Add the equations.

Step 4: Solve for x. Step 5: Find the y-value by substituting in 3 for x in either equation. How do inequality signs work? Multiplying each side of an inequality by a negative number reverses the direction of the inequality symbol.

Dividing each side of an inequality by a negative number reverses the direction of the inequality symbol. How do you write interval notation? How to Determine Linear Equations. How to Do Math Problems in Algebra 1. How to Calculate the Equation of a Line. How to Solve Absolute Value Inequalities. How to Find the Domain of a Function Defined by an How to Compare Negative Fractions. How to Solve for a Variable. How to Get the Value of a Letter in Algebra 1. How to Find the Zeros of a Function.

Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign. One very important implication of this rule is: You cannot divide by an unknown i. There are plenty of instances where you will know the sign of a variable and as a result, you can multiply or divide and know for sure whether you must flip the inequality sign.