Question

what value of \\(x\\) is in the solution set of the inequality \\(8x - 6 > 12 + 2x\\)?

-1
3
5
0

Explanation:

Identify the given inequality

We are given the linear inequality:

$$8x - 6 > 12 + 2x$$

We need to find which of the given values of \(x\) (\(-1\), \(3\), \(5\), or \(0\)) satisfies this inequality.

Solve the inequality

Using Solving Linear Inequalities and Inequality Properties, we isolate the variable \(x\). First, subtract \(2x\) from both sides:

$$6x - 6 > 12$$

Next, add \(6\) to both sides:

$$6x > 18$$

Finally, divide both sides by \(6\):

$$x > 3$$

Evaluate the given options

The solution set contains all real numbers strictly greater than \(3\). Let's test each option:

• For \(x = -1\): \(-1 > 3\) is False.
• For \(x = 0\): \(0 > 3\) is False.
• For \(x = 3\): \(3 > 3\) is False (since the inequality is strict).
• For \(x = 5\): \(5 > 3\) is True.

Therefore, \(5\) is in the solution set.

Answer:

• -1
• 3
• 5 (Correct answer)
• 0