How To Solve Inequality Problems

How To Solve Inequality Problems-5
Try inserting sample values for GRC and HHC and see what happens when each drops to half its value.The correct relationship is the value of GRC So Ellie’s current age must be at least 11 if she will be able to vote in 7 years.The inequality has been reversed, and AC A businesswoman is comparing the value of two stocks, Goodman Rent-a-Car (GRC) and Harris Home Construction (HHC).

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It holds true for the flag as it was designed in 1777 (13 stars, 50 ≥ 13), as it looked in 1850 (30 stars, 50 ≥ 30), and how we see it today (50 stars, 50 ≥ 50).

relationships; this symbol indicates that the point on the number line is not included within the range of possible values for the inequality.

The Properties of Inequality can help us understand how to add, subtract, multiply, or divide within an inequality. You went through the steps of isolating u correctly, but you flipped the inequality when you didn’t have to. The symbol only flips when you divide or multiply by a negative number. Inequalities model problems that have a range of answers.

The symbol only flips when you divide or multiply by a negative number. They can be mapped along a number line, and they can be manipulated to simplify or solve them.

To solve this problem, we want to isolate the variable y, just as we would to solve an equation.

We can do this by dividing both sides of the inequality by -4.In a certain number of years from now, will Adam still be older than Bernard? Adam is older to begin with, and they are aging the same amount.In algebraic fashion, you could represent this inequality as: The age example can help you make sense of this relationship as well: if Adam is older than Bernard now, then five years ago Adam was also older than Bernard (because Bernard was also five years younger).From the Division Property of Inequality, we know that if we divide both sides of an inequality by a number less than 0, the inequality will “flip,” so we need to be careful to change the symbol.Solving inequalities, then, is very similar to solving equations—what we do to one side we need to do to the other side in order to maintain the “balance” of the inequality. You subtracted 4 from both sides instead of adding 4, and then you flipped the inequality when you didn’t have to.When solving inequalities, it is important to follow the Properties of Inequality: These properties help us manage the inequality symbol properly.The inequality is maintained by addition and subtraction, and by multiplication and division with positive numbers.The important thing about inequalities is that there are multiple possible solutions.For example, the inequality “50 ≥ the number of stars on any United States flag” is a true statement for every American flag ever flown—no flag has had over 50 stars.You could represent this inequality as: If we take the same two numbers and multiply them by -0.5, something different happens.The resulting value of AC (-2.5), is further to the left than the value of BC ( -1).

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