Solving Equations

You will generally find the last operation is the first thing to undo. Imagine you are computing the equation on a calculator. The last operation you would type is likely to be the first operation to undo. Let’s look at a really big and messy example; try to spot how we’re working backwards to undo it!

Big Messy Example:

Solve for x: 2(x - 1)² + 3 = 21

Solution:

Subtract 3 from both sides:	2(x - 1)2 + 3 - 3 = 21 - 3
or:	2(x - 1)2 = 18
Divide both sides by 2:
or:	(x - 1)2 = 9
Square root of both sides:
or:	x - 1 = 3
Finally add 1 to both sides:	x + 1 - 1 = 3 + 1
or:	x = 4

Check:

Substitute 4 into the original equation:

2•(4-1)² + 3 = 21

2•32 + 3 = 21

2•9 + 3 = 21

21 = 21 Yes!