Question

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Express the statement as an inequality

g. The quotient of p and q is at most 6
1. p/q ≤ 6
2. p/q < 6
3. p/q = 6
4. p/q > 6
5. p/q ≥ 6

h. The reciprocal of w is at least 8
1. 1/w > 8
2. 1/w ≥ 8
3. 1/w = 8
4. 1/w < 8
5. 1/w ≤ 8

i. The absolute value of x is greater than 6
1. |x| = 6
2. |x| ≤ 6
3. |x| ≥ 6
4. |x| > 6
5. |x| < 6

Answer 1

Step-by-step explanation: g. The quotient of p and q is at most 6

Answer: 1. p/q ≤ 6

h. The reciprocal of w is at least 8

Answer: 2. 1/w ≥ 8

i. The absolute value of x is greater than 6

Answer: 4. |x| > 6

Answer 2

g. Answer: 1. p/q ≤ 6

h. Answer: 2. 1/w ≥ 8

i. Answer: 4. |x| > 6

Explanation:

g. The quotient of p and q is at most 6. To express this statement as an inequality, we need to use the inequality symbol for "less than or equal to", which is denoted as "≤". The correct inequality is p/q ≤ 6, which means that the value of p divided by q should be less than or equal to 6.

h. The reciprocal of w is at least 8. To express this statement as an inequality, we need to use the inequality symbol for "greater than or equal to", which is denoted as "≥". Since we are dealing with the reciprocal of w, which is 1/w, the correct inequality is 1/w ≥ 8. This means that the value of 1/w should be greater than or equal to 8.

i. The absolute value of x is greater than 6. The absolute value of a number is always non-negative, so it can't be less than 6. Therefore, we need to use the inequality symbol for "greater than", which is denoted as ">". The correct inequality is |x| > 6, which means that the absolute value of x should be greater than 6.