graph is correct? (The green region is the shaded area).%0D%0A%0D%0A4x+14≤38%0D%0A4%0D%0A𝑥%0D%0A+%0D%0A14%0D%0A≤%0D%0A38%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0ASubtract 14 and divide by 4, flip the inequality sign x ≥6%0D%0A𝑥%0D%0A %0D%0A≥%0D%0A6%0D%0A %0D%0ASubtract 14 and divide by 4, flip the inequality sign x ≥6%0D%0A𝑥%0D%0A %0D%0A≥%0D%0A6%0D%0A %0D%0A%0D%0ASubtract 14 and divide by 4, x ≤6%0D%0A𝑥%0D%0A %0D%0A≤%0D%0A6%0D%0A %0D%0ASubtract 14 and divide by 4, x ≤6%0D%0A𝑥%0D%0A %0D%0A≤%0D%0A6%0D%0A %0D%0A%0D%0ASubtract 14 and multiply by 4, x ≤6%0D%0A𝑥%0D%0A %0D%0A≤%0D%0A6%0D%0A %0D%0ASubtract 14 and multiply by 4, x ≤6%0D%0A𝑥%0D%0A %0D%0A≤%0D%0A6%0D%0A %0D%0A%0D%0ASubtract 14 and divide by 4, x ≤6%0D%0A𝑥%0D%0A %0D%0A≤%0D%0A6%0D%0A

Answer 1

Let's analyze the inequality you provided:

\[ 4x + 14 \leq 38 \]

To solve for \( x \), follow these steps:

1. Subtract 14 from both sides: \[ 4x \leq 38 - 14 \] \[ 4x \leq 24 \]

2. Divide both sides by 4: \[ x \leq \frac{24}{4} \] \[ x \leq 6 \]

Thus, the correct inequality is

\[ x \leq 6 \]

Now, regarding the shaded area (the green region) on a graph:

• If the graph represents the solution set for \( x \leq 6 \), then the correct representation would be a line that includes \( x = 6 \) and extends to the left, indicating that all values less than or equal to 6 are part of the solution.

So, based on the options provided in your responses:

• The correct information is:
  • Subtract 14 and divide by 4, \( x \leq 6 \)

If the green region (shaded area) in the graph corresponds to \( x \leq 6 \), then it is correct. If it represents something different (for example, shading to the right of 6), then it would not be correct.

Please ensure the graph aligns with the solution \( x \leq 6 \).