# 5 Solving equations

Solving by inspection

The most simplest way to solve an equation is by inspection, which is a guessing technique.

For example, to solve $x+2=3$. By trying out different numbers for $x$, you’ll determine $x=1$

Solving by inverse operations

A more effective way of solving questions is the inverse operation method. It is necessary to know that:

• Addition and subtraction are inverse operations
• Multiplication and division are inverse operations
• Square and finding the square root are inverse operations

For example, to solve $2x+1=11$, we start on the RHS and apply inverse operations. The inverse of “-1” is “+1”, so we “+1” to both sides. We must do it to both sides because the left hand side is equal to the right hand side, so if we don’t do the same thing to both sides, the 2 sides are no longer equal! This will give us $2x+1 -1=11 -1$, or simplifying, $2x=10$. The inverse operation of “*2” is “/2”, so we will “/2” on both sides. This gives us $2x/2=10/2$, or otherwise, $x=5$.

Again, solving equations that are provided by word questions are by far the hardest, as in all mathematics.