Which of the following correctly solves the linear inequality 2/5x+2≤4 ?(1 point) Responses x≤8 x less-than-or-equal-to 8 x≥8 x greater-than-or-equal-to 8 x≥3 x greater-than-or-equal-to 3 x≤5

Answer 1

To solve the inequality \( \frac{2}{5}x + 2 \leq 4 \), we can follow these steps:

1. Subtract 2 from both sides: \[ \frac{2}{5}x \leq 4 - 2 \] \[ \frac{2}{5}x \leq 2 \]

2. Multiply both sides by \(\frac{5}{2}\) to isolate \(x\) (since \(\frac{5}{2}\) is positive, the direction of the inequality does not change): \[ x \leq 2 \cdot \frac{5}{2} \] \[ x \leq 5 \]

The correct solution to the inequality \( \frac{2}{5}x + 2 \leq 4 \) is \( x \leq 5 \).

So, the correct answer is:

x≤5