 ## What Value of X is in the Solution Set of the Inequality 8x – 6 > 12 + 2x? –1 0 3 5

When solving inequalities, it’s important to determine which values of x satisfy the given inequality. In this case, we’ll be looking at the inequality 8x – 6 > 12 + 2x. By simplifying and rearranging the terms, we can find the solution set for x.

To start, let’s combine like terms by subtracting 2x from both sides of the inequality: 8x – 2x – 6 > 12. This gives us 6x – 6 > 12. Next, let’s add 6 to both sides to isolate the variable: 6x >18. Finally, dividing both sides by 6 yields x >3.

Therefore, in order for the inequality to hold true, x must be greater than three. Any value of x that is greater than three will be part of the solution set.

## Understanding the Inequality

Let’s dive into understanding the inequality 8x – 6 > 12 + 2x. This type of inequality involves variables, coefficients, and comparison symbols that determine the range of values for which the inequality holds true. By breaking down each component and applying simple algebraic techniques, we can find the solution set.

First, let’s focus on simplifying both sides of the inequality. We combine like terms by subtracting 2x from both sides to eliminate variables on one side: 8x – 2x – 6 > 12. This gives us 6x – 6 > 12.

To isolate x, we need to get rid of the constant term (-6) on the left side of the inequality. Adding 6 to both sides yields: 6x – 6 + 6 > 12 + 6. Simplifying further, we have:

⇨   (6x) > (18)

Now it becomes clear that our goal is to find out what value(s) of x makes this statement true. To do so, we divide both sides by the coefficient in front of x (which is positive), ensuring that we maintain the directionality of the inequality:

⇨   (6x)/6 > (18)/6

Simplifying further gives us:

⇨   x >3

So, in this case, any value greater than three satisfies our original inequality.

Understanding inequalities allows us to analyze relationships between variables and make informed decisions based on their ranges. It also helps solve real-world problems where multiple factors come into play. By applying algebraic techniques and logical reasoning, we can determine the solution set for a given inequality. In this case, x > 3 is the key to unlocking the values that make the inequality true.

## Simplifying the Inequality

### Solving the Inequality

To find the value of x in the solution set of the inequality 8x – 6 > 12 + 2x, we need to simplify and solve for x. Let’s break down the steps involved in this process.

First, let’s start by combining like terms on each side of the inequality. We have 8x – 6 on one side and 12 + 2x on the other. To combine these terms, we can subtract 2x from both sides. This will eliminate the variable term from one side and allow us to isolate x.

After subtracting 2x from both sides, we get:

8x – 2x – 6 >12

Simplifying further, we have:

6x – 6 >12

Now that we’ve simplified the inequality, our next step is to isolate x.

### Isolating the Variable

To isolate x, we need to get rid of any constants or terms that are not directly attached to it. In this case, we have a constant term (-6) on the left side of the inequality that needs to be eliminated.

To do so, let’s add 6 to both sides of the equation:

6x – 6 + 6 >12 + 6

Simplifying further:

6x >18

Now that we have isolated x on one side of the inequality sign, we can move on to solving for its value.

### Combining Like Terms

The final step is dividing both sides by coefficient (the number multiplying with x) which is “6” in this case. By doing so, we’ll obtain a simplified solution for x.

Dividing both sides by “6”, we get:

(6/5)x >3

And simplifying further,

𝑥>𝟑/𝟔

So, the value of x in the solution set of the inequality 8x – 6 > 12 + 2x is x > 3/6 or equivalently x > 1/2.

By following these steps – simplifying the inequality, isolating the variable, and combining like terms – we were able to determine the range of values for x that satisfy the given inequality. Remember to always double-check your work and ensure you’ve followed each step accurately when solving inequalities.