Hi there! For this It All Adds Up math lesson, I wanted to discuss how to solve and graph inequalities. They are extremely similar to solving multi-step equations.

Let’s start with this inequality:

## 3a + 8 > 14 + a

We solve this as we would a normal multi-step equations. We subtract the 8 from both sides and subtract one a from each side. That leaves us with this inequality:

## 2a > 6

We then divide both sides by two to find out that a is greater than 3.

With inequalities, though, most are not that simple, especially when dealing with negative numbers. Let’s take the second inequality from above, and say that we changed it to this:

## -2a > 6

We would solve this the same way, but this time dividing by negative two. But when multiplying or dividing by a negative number, we must then change the direction of the sign. The solution to that particular inequality would therefore be this:

## a < -3

In a way, this makes sense, since we changed the 3 to a negative number.

This would work out the same way if the sign was a greater than or equal to sign, and the greater than sign would simply change directions. The only thing different about a greater/lesser than or equal to symbol is that it effects how we graph the inequality.

We graph inequalities using a line bar, such as this one:

We graph an inequality to find out which numbers could be a solution to the inequality. If the inequality is less than the variable, the line moves left. If the inequality is greater than the variable, the line moves right.

When we are using regular greater than or lesser than symbols, we use an open bubble. When we are using greater/lesser than or equal to symbols, we use a closed bubble.

Here is a solved inequality and its corresponding graph:

## a > -3

This shows that any number beyond the bubble is a possible solution to finding the value of a. We would simply fill in the bubble if the inequality was using a greater than or equal to symbol, which means that -3 could also be the value of a.

Now that you know how to solve and graph inequalities, try solving and graphing this one, and check your answers on August 6th.

## 4a -5 ≥ -5a + 76

There will not be an It All Adds Up post next week as I will be on vacation, but when it returns on August 14, I will be discussing how to factor out an equation.

Thanks so much for reading!

Gabe