Consider the inequality.

59w≥8

Which step is needed to solve this inequality?

(1 point)
Responses

Add 59
to both sides of the inequality.
Add 5 ninths to both sides of the inequality.

Subtract 59
to both sides of the inequality.
Subtract 5 ninths to both sides of the inequality.

Multiply 59
on both sides of the inequality.
Multiply 5 ninths on both sides of the inequality.

Divide 59
on both sides of the inequality.
Divide 5 ninths on both sides of the inequality.
Question 2
Determine the solution to the inequality.(1 point)
Responses

w≥1425
w is greater than or equal to 14 and 2 fifths

w≥445
w is greater than or equal to 4 and 4 fifths

w≥859
w is greater than or equal to 8 and 5 ninths

w≥749
w is greater than or equal to 7 and 4 ninths
Question 3
How should the solution of the inequality be graphed?(1 point)
Responses

Open circle, shade right
Open circle, shade right

Open circle, shade left
Open circle, shade left

Closed circle, shade right
Closed circle, shade right

Closed circle, shade left
Closed circle, shade left
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1 answer

Let's solve the inequality step by step.

Question 1: Which step is needed to solve the inequality?

The inequality to solve is:

\[ 59w \geq 8 \]

To solve for \( w \), we need to isolate \( w \) on one side. The best way to do that here is to divide both sides of the inequality by 59:

\[ w \geq \frac{8}{59} \]

So the correct response from the options is:

Divide 59 on both sides of the inequality.


Question 2: Determine the solution to the inequality.

Now let's calculate:

\[ \frac{8}{59} \approx 0.135593 \]

This does not match any of the options perfectly, but we can express \( \frac{8}{59} \) in decimal or fraction terms.

To check options:

  1. w ≥ 1425 - doesn't match.
  2. w is greater than or equal to 14 and 2 fifths - doesn't match.
  3. w ≥ 859 - doesn't match.
  4. w ≥ 749 - doesn't match.

The options provided do not show \( w \geq \frac{8}{59} \). If \( \frac{8}{59} \) were expressed as a decimal, it could be approximated but not directly represented in fractional terms provided.

Assuming we take \( \frac{8}{59} \) as the main value, none of the choices align well with it. However, from none of the given answers directly corresponding, the closest could be interpreted as a misalignment on representation.


Question 3: How should the solution of the inequality be graphed?

Because the inequality is \( \geq \), we have a closed circle on the graph, representing that \( w \) can equal \( \frac{8}{59} \) and include all values greater than that.

Thus, the correct choice would be:

Closed circle, shade right.


To summarize:

  1. Divide 59 on both sides of the inequality.
  2. None of the given exact responses match \( \frac{8}{59} \).
  3. Closed circle, shade right.