Graph Inequality

Question

Graph the solution of 2x -2 greater than or equal to 2 on a number line

Answer 1

Chris,

 

This equation looks like this:

 

2x-2 ≥ 2

 

Remember when working with inequlities that the greater than/less than or greater than or equal to/less than or equal to sign stands in for the equal sign. So, that means that you have one set of information on the left, and one set of information on the right. You write  out the first bit of information on the left, next you write the sign indicated by the written equation (in this case, greater than or equal to), then you write the second bit of information on the right (which is 2).

 

 

In order to answer this question you must use Algebra to isolate the x. Remember, when you are working with variables it is sort of like following PEMDAS in reverse. This means you start with subtraction/addition, then deal with multiplication/division, followed by exponents, and parenthesis. So, for this question we want to start working with -2. We can add two to the left, but you must also add two to the right side. (This is because we need to perform the same operation on both sides of the equation in order to maintain an equivalent expression. Otherwise, we will end up with a new expression, and this will not help us solve for x.)

 

So, we have this expression:

 

2x ≥ 4

 

Next, we can divide both sides by two. This will leave us with the following expression: 

 

x ≥ 2

 

Now we can graph this answer on a number line. We know that this expression has a greater than OR equal to sign which means we need to make a solid dot at the number two on our number line. Then we should draw an arrow that extends towards the right side of this solid dot. We draw an arrow towards the right because that will point towards values that are greater than two, and our simplified equation says that x is equal to or greater than 2.