Question

Graph the solution set of: 2x - 4 ≤ 8 and x + 5 ≥ 7​

Answer 1

First of all, we have to solve both inequalities: for the first one we have

`2x-4\leq 8`

Add 4 to both sides

`2x\leq 12`

Divide both sides by 2:

`x\leq 6`

For the second one we have

`x+5\geq 7`

Subtract 5 from both sides

`x\geq 2`

So, our solution set is composed by all numbers that are less than 6 (included) and more than 2 (included). Using all possible notations, we have

`[2,6],\quad 2\leq x \leq 6,\quad \{x \in \mathbb{R}: 2\leq x \leq 6\}`

Answer 2

x ≤ 6 and x ≥ 2

Explanation:

For now, we will start with doing each problem at a time. Here is your equation:

2x - 4 ≤ 8

First, you want to get the variable by itself. So, you add 4 to both sides. It will look like this:

2x - 4 ≤ 8

+ 4 + 4

The four being added on the left side cancels out, and you add 4 to 8. Now, it should look like this:

2x ≤ 12

Next, you want the x by itself. So, you would divide both sides by 2.

2x ≤ 12

/2 /2

2 divided by 2 cancels out, and 12 divided by 2 equals 6. Now, you have a final answer of:

x ≤ 6

But, you now have to do the other one!

Here is what you start off with:

x + 5 ≥ 7

First, you want the variable side by itself. So, you subtract 5 from both sides.

x + 5 ≥ 7

- 5 -5

Now, you have this:

x ≥ 2

Because the variable is already by itself, you don't need to do any more division and this is you final answer. Now put both answers you got together which equals:

x ≤ 6 and x ≥ 2