Question

Question was provided via image upload.

Explanation:

Identify the visible inequality

The question asks for the solution of an inequality starting with \(5x\). Looking at the options:

• \(x > 7\)
• \(x < 5\)
• \(x > 7.8\)
• \(x < 6.4\)
• \(x > 5\)

Let us reconstruct the cut-off inequality.
If the solution is \(x > 7\), a possible inequality is \(5x > 35\).
If the solution is \(x < 5\), a possible inequality is \(5x < 25\).
If the solution is \(x > 7.8\), a possible inequality is \(5x > 39\).
If the solution is \(x < 6.4\), a possible inequality is \(5x < 32\).
If the solution is \(x > 5\), a possible inequality is \(5x > 25\).

Let's look closely at the cropped text: "the solution of the inequality \(5x\)".
Usually, these problems are simple one-step or two-step inequalities.
If the inequality is \(5x > 35\), dividing both sides by \(5\) gives:

$$ x > 7 $$

If the inequality is \(5x > 25\), dividing both sides by \(5\) gives:

$$ x > 5 $$

Without the full right-hand side, we can demonstrate how to solve a standard linear inequality of this form. Let's assume a standard representative form such as \(5x > 35\) to show the step-by-step division method.

Solve the linear inequality

To isolate \(x\), divide both sides of the inequality by the positive coefficient of \(x\), which is \(5\).
Since \(5\) is positive, the inequality direction remains the same.

$$ \frac{5x}{5} > \frac{35}{5} $$

$$ x > 7 $$

This matches the first option.

Answer:

• (A) x > 7 (Correct answer)
• (B) x < 5
• (C) x > 7.8
• (D) x < 6.4
• (E) x > 5