Equations

Lesson

Suppose a person is holding a puppy steps on a scale.

One way to solve this is to use algebra. Let $x$`x` be the weight of the puppy.The number that shows on the scale is $75$75kg. If the person weighs $70$70kg, how much does the puppy weigh?

Because we know that $\text{Person }+\text{Puppy }=75$Person +Puppy =75, then $70+x=75$70+`x`=75.

To solve for $x$`x`, for these simple one step problems, we have two choices.

1. We can subtract $70$70 from both sides.

So $x+70-70=75-70$`x`+70−70=75−70, which simplifies to $x=5$`x`=5.

or

2. We can solve by inspection, we might just know that $70+5=75$70+5=75. Valuing what you can see and know is really important, and mathspace will do that. Remember though, that the process we are learning here, (ie reversing operations by doing the same to both sides) will help us with harder problems later.

You've seen how to solve equations involving addition and subtraction. But how do we solve an equation like $5x=5$5`x`=5? The process is as simple as before. But now, instead of adding or subtracting a number to or from both sides, you have to divide both sides by a number. In this case if you divide both sides of $5x=5$5`x`=5 by $5$5, you will get $x=1$`x`=1. The process for solving equations of this form is always the same.

Solve: $x-4=10$`x`−4=10

Solve: $\frac{x}{8}=6$`x`8=6

Solve: $-x=3$−`x`=3