Mathematics Magazine for Grades 1-12  

Grade 8

Theory:

Solving an Inequality

An inequality is similar to an equation. There are two expressions separated by a symbol that indicates how one expression is related to the other. In an equation such as 7x = 49, the = sign indicates that the expressions are equivalent. In an inequality, such as 7x > 49, the > sign indicates that the left side is larger than the right side.

To solve the inequality 7x > 49, we follow the same rules that we did for equations. In this case, divide both sides by 7 so that x > 7. This means that x is a value and it is always larger than 7, and never equal to or less than 7.

The "less than" symbol (<) may also be seen in inequalities.

Solutions from the Previous Issue:

1.        Which number is 100 more than 99,999?

Solution:       99,999 + 100 = 100,099

2.      The regular price of a computer game is $49.95. Which of the following sale prices would result in the lowest price for the computer game?

A. $8 less than the regular price

B. 20% discount on the regular price

C. 1/4 reduction on the regular price

D. 85% of the regular price

Solution:       For Case A            $49.95 - $8 = $41.95

                            Case B                    $49.95 – 20% x $49.95 = $39.96

                            Case C                    $49.95 –1/4 x $49.95 = $37.4625

                            Case D                   $49.95 x 85% = $42.4575

Case C results in the lowest prince

3.        The product of 9/10 and 8/9 is…

Solution:

4.      Use the figure below to answer; what is the measure of angle A?

Solution:       C = 180⁰ – 130⁰ = 50⁰

A + B + C = 180⁰

A + 70⁰ + 50⁰ = 180⁰

A = 60⁰

5.      Which of the following best describes the meaning of π?

A. The measurement of the circumference of a circle

B. The measurement of the diameter of a circle

C. The ratio of the circumference of a circle to its diameter

D. The ratio of the area of a circle to its circumference

Solution:       C. The ratio of the circumference of a circle to its diameter

Proposed Exercises:

1.        Rectangle MATH has vertices M(1,2), A(1,-3), T(-5,-3), and H(-5,2). What are the coordinates of the rectangle after a translation 2 units right and 4 units down?

2.        Suppose the radius of a cone is doubled. How could you change the height so that the volume will remain the same?

3.        The two solids have about the same volume. Jeff says that the surface area of the cylinder is less than the surface area of the rectangular solid. Karen disagrees. Who is correct?

4.        Pipe A can fill an empty tank in 8 hours. Pipe B can fill the tank in 12 hours. If both pipes are used to fill the tank, how long will it take to fill the tank? Give your answer to the nearest minute.

Read more on the written version of the publication.