We can use our inverse property of addition subtracting 4 from both sides. But there's a faster way. In words, the variable x is greater than or equal to Notice how the sign of the inequality flipped when we multiplied by negative one. Much like when you divide by a negative number, the sign of the inequality must flip! Here's why:. Imagine comparing the numbers 5 and 3. Obviously this is wrong! 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. You can also consider this with a number line. The solution to the set of inequalities is the overlapping graphical area. Get Link. You cannot divide by y or 5y since you do not know whether y is negative or positive and, as such, you do not know whether to flip the inequality. These kinds of problems take some practice, so don't worry if you aren't getting it at first!
Keep at it and it will eventually become second nature. You also often need to flip the inequality sign when solving inequalities with absolute values. How to Divide Negative Fractions. How to Solve Double Inequalities.
Standard Form of a Linear Equation. How to Solve Inequalities With Fractions. How to Divide Negative Numbers. How to Determine Linear Equations. Don't flip. Flip if they are the same sign. Note, however, in your question you misused the reciprocal.
In algebra, there are rules for what you can do to an equation or inequality to make sure it stays true. For example, you can add the same number to both sides of the equation, or you can multiply both sides of the equation by the same number except zero.
You can take the reciprocal of an equation just by performing several multiplication and division operations in a row. Here's why:. Sign up to join this community. The best answers are voted up and rise to the top.
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