15) Solve the inequality and graph: 2x − 2 <− 12 or 2x + 3 > 7

Answer 1

To solve the inequality 2x - 2 < -12, we can begin by adding 2 to both sides of the inequality:

2x - 2 + 2 < -12 + 2

Simplifying, we have:

2x < -10

Next, we can divide both sides of the inequality by 2 to solve for x:

2x/2 < -10/2

Simplifying further, we get:

x < -5

Now, let's solve the second part of the inequality, 2x + 3 > 7. We can start by subtracting 3 from both sides:

2x + 3 - 3 > 7 - 3

Simplifying, we have:

2x > 4

Finally, we can divide both sides by 2 to solve for x:

2x/2 > 4/2

Simplifying further, we get:

x > 2

So, the solutions to the inequality are x < -5 or x > 2.

Now let's graph the inequality on a number line:

On the number line, mark a point at -5 and draw an open circle to represent x < -5. Then draw an arrow to the left, indicating that all numbers less than -5 are solutions to the inequality.

Next, mark a point at 2 and draw an open circle to represent x > 2. Then draw an arrow to the right, indicating that all numbers greater than 2 are solutions to the inequality.

The graph should look like this:

-5 2
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