Question

Ben needs to walk at least 5 miles per week each time he walks he covers 3/4 miles if he has already walked 2 miles this week how many more walks x does he need to reach or exceed his goal
2x + 3/4 ≥ 5
2x + 5 ≥ 3/4
2x + 5 ≤ 3/4
3/4x + 2 ≤ 5
3/4x + 5 ≥ 2
3/4x + 2 ≥ 5
2x + 3/4 ≤ 5

Answer 1

To determine how many more walks (x) Ben needs to meet his goal of walking at least 5 miles in a week, we can set up the inequality based on the information provided.

1. **Current Distance Covered**: Ben has already walked 2 miles.
2. **Distance Covered Per Walk**: Each time Ben walks, he covers \( \frac{3}{4} \) miles.

We want to find how many walks Ben needs to satisfy the condition that his total distance is at least 5 miles. Hence, the inequality we need to solve is:

\[
2 + \frac{3}{4}x \geq 5
\]

Next, we can solve this inequality step by step:

1. Subtract 2 from both sides:
\[
\frac{3}{4}x \geq 5 - 2
\]
\[
\frac{3}{4}x \geq 3
\]

2. To isolate \(x\), multiply both sides by the reciprocal of \( \frac{3}{4} \) (which is \( \frac{4}{3} \)):
\[
x \geq 3 \cdot \frac{4}{3}
\]
\[
x \geq 4
\]

This means Ben needs to walk at least **4 more times** to reach or exceed his goal of 5 miles this week.