These worksheets teach your students how to solve and graphically express equations that contain inequalities.

A rational value is any number that can by formed by taking the quotient of two integers. This basically tells us that it does not have a fractional portion to it. Solving rational inequalities is very much like solving equations, which we should have a good handle on by this point. You start by simplifying the inequality that you are given. The next step is to evaluate it at a point of interest, the x-axis (noted as x = 0) is always nice. The last thing to do is run test points to see where it lies.

We can solve rational inequalities as we resolve the polynomial inequalities. But you will find denominators in rational figures. Therefore, it may have some areas where you can't define them. You have to be a little bit careful while solving the problems. You will find zeroes under the numerator and undefined points under denominator while solving rational inequality. You can divide the number lines into intervals by using zeroes and uncleared points. As a result, you will find the sign of the rational on each range. Solve: x2 + 3x + 2/x2 - 16 ≥ 0 Factorize the following;x2 + 3x + 2/x2- 16 = (x + 2)(x+1)/(x+4)(x-4) When you find zero nominators of polynomial fraction, you will keep the nominator equal to zero and the solution like the following one; (x+2)(x+1) = 0, x+2 = 0 or x + 1 = 0, x = -2 or x = -1 You will apply the same rule in the following solution; (x+4)(x-4) = 0, x+4 = 0 or x + 4 = 0, x = -4 or x = -4 Divide the number line into five intervals by the above answers that are -4, -2, -1, and 4. (-infinity - 4), (-4,-2), (-2,-1),(-1,4), and (4, +infinity). These worksheets explain how to solve and graphically express (on number lines) equations containing inequalities. The lesson specifically show students how to place these values on a number line.



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Rational Inequalities Lesson and Practice

You will learn to express these values on number lines. A sample problem is solved and two practice problems are provided.

Worksheet

Students are given equations and will express their solutions on number lines. Nine problems are provided.

Practice

You need to express all of these graphically. Give yourself plenty of space.

Review and Practice

When you solve this make sure to test all of the points that are available. On this page, a sample problem is solved and six practice problems are provided.

Rational Inequalities Quiz

Students demonstrate their proficiency with this skill in a nice area. Nine problems are provided.

Topic Check

You will bring these things to life and make them start to dance.

Inequalities Lesson

Write an inequality for each situation. Use a variable. Minimum passing marks is 36 and maximum marks are 100.

Lesson and Practice

Students will write an inequality for each picture using a variable. A sample problem is solved and two practice problems are provided.

Worksheet

Write an inequality for each situation. Use a variable if needed.

Skills Practice

You will express this on a numbers line and you can also draw pictures.

Inequalities Drill

Which of the given number are solutions to the inequalities?

Warm Up

You want to build a fenced square-shape area for walking. The perimeter of the square can be a maximum of 64 meters long.