Solving Algebraic Equations Part 1

Algebra is daunting for many high school students. In elementary school the focus is on arithmetic so their perception of mathematics is completely blown out of the water when letters of the alphabet are thrown into the mix. For many, the idea of using letters and numbers together places a block in their minds which some never get over. It is a shame but could be remedied by taking this into consideration when the topic is first introduced.

This article deals specifically with solving equations. There are only two types of equations that high school students are required to solve and not the huge number many imagine. By realising this the student's perception of the topic is softened and and its mastery made more achievable.

The two types of equations are “Wall Type” or “Escalator Type”. These are not the labels used in school but creations of the author for the purpose of identification. This article deals with solving the “Escalator Type” equation.

An Escalator Type equation in algebra has only two terms and can be written with the equal sign between them.

Here are four examples:

3X = 8

5a/3 = 9

3x/4 = 2/5

ax² = k

By turning the 'equal' sign into an escalator the student is reminded that only diagonal movement of numbers and letters across the 'equal' sign is allowed. Vertical movement across the equal sign is prohibited.

Any whole number can be written over 1 and this is done before proceeding.

When a number or letter is moved the number 1 is left behind like a calling card. By doing this the symmetry of the equation is preserved and so easier for the student to follow each step.

When a number or letter is moved it multiplies with the number or letter it is placed beside.

The question asks to solve an equation and this means to find out what number the letter represents. The object of the exercise is to isolate the letter you are asked to find by following the rules for that type of equation.

The proof of the pudding is in its eating. So now it is your turn.

Please try the following questions and check your answers with the answers provided below.

Good luck!