Mathematics Magazine for Grades 1-12  

9/2004

Grade 7

Theory

Solving an Equation

An equation is a mathematical statement that has two expressions separated by an equal sign. The expression on the left side of the equal sign has the same value as the expression on the right side.One or both of the expressions may contain variables. Solving an equation means manipulating the expressions and finding the value of the variables.For example solve the equation: 8x-2=14
To keep both sides of an equation equal, we must do exactly the same thing to each side of the equation. First, add two to each side of the equation so that

8x –2 + 2= 14 + 2 or 8x = 16. If we multiply (or divide) one side by a quantity, we must multiply (or divide) the other side by that same quantity.
In order to solve this equation we would divide both sides by 8. The equation would become 8x/8 = 16/8. When simplified, this would become x = 16/8 or x = 2. It is possible to substitute the value of x back into the original equation 8 2 – 2 = 14.

Solutions from the Previous Issue:

Calculate:

1.        2² - ( - 13) =

Solution: 2² - ( - 13) = 4 + 13 =17

2.        15.5 + (-24.8) (-6.2) - 27 + 4² =

Solution: 15.5 + (-24.8) (-6.2) - 27 + 4² =15.5 + 4 – 27 + 16 = 8.5  

3.        15.7 + (-47) 15.7=

Solution: 15.7 + (-47) 15.7= 15.7 [1 + (-47)] = 15.7 (-46) = - 722.2

4.        49 – [-27.4 (-13.7) - 18.1 + 43] =

Solution: 49 – [-27.4 (-13.7) - 18.1 + 43] = 49 – (2- 18.1 + 43) = 49 – (2- 18.1 + 43) = 49 - 26.9 = 22.1

Proposed Exercises:

1.        What is the area of a triangle with base 5 1/2 cm and height 8 1/2 cm?

2.        What is the length of the base of a triangle with height 3 m and area 13 3/4 m²?

3.  8.64 x 10^-12

4.  3.7 x 10¹⁰