Mechanical Trades: Basic Algebra – Study Guide 8 FB/2015 Page 1
Basic Algebra
In basic algebra, letters represent numbers. It is important to collect same letters together when possible.
For example: 3x + 2x + 6x should be written as 11x (there are 11 x’s altogether)
5y – 3y should be written as 2y
1x is usually written as x (the 1 is assumed)
If you are given the value (number) for the letter, you can substitute that value for the letters to answer the equation.
For example: Solve
2x3
when
4x
Simply substitute 4 for the
x
and solve.
3x + 2
3 (4) + 2
12 + 2
= 14
An equation is solved when the unknown letter is isolated on one side of the equal sign. When isolating x, the
equation must be kept balanced. To maintain balance, you must always do the same thing to both sides of the
equation.
For example: x + 3 = 10
3 is being added to
x
, so do the opposite to both sides and subtract 3 from both sides to
isolate
x
. On the left side, 3 - 3 is 0, leaving just the x on the left.
x + 3 = 10
–3 –3
x = 7
Practice: a) Solve x – 6 = 4
6 is being subtracted from
x
so add 6 to both sides to isolate
x
. Again,
–6 +6 = 0, leaving just x on the left.
x – 6 = 4
x – 6 + 6 = 4 + 6
x = 10
