When the value of r is 23, the equation 3r−47.5=21.5 is a true statement. Which of the following values of r makes the inequality 3r−47.5>21.5 a true statement?

Answer 1

To solve the equation 3r - 47.5 = 21.5, we can first add 47.5 to both sides to get 3r = 69. Then, we divide both sides by 3 to find that r = 23.

To solve the inequality 3r - 47.5 > 21.5, we can follow similar steps. First, we add 47.5 to both sides to get 3r > 69. Then, we divide both sides by 3 to find that r > 23.

Since the value of r that satisfies the inequality is greater than 23, there are infinitely many possible values of r that make the inequality true. For example, r could be 24, 25, 26, and so on.

Answer 2

Which of the following values for x makes the inequality 4x+1−−−−−√ ≤5.83 true?

Answer 3

To solve the inequality 4x + 1 ≤ 5.83, we can first subtract 1 from both sides to get 4x ≤ 4.83. Then, we divide both sides by 4 to find that x ≤ 1.2075.

Therefore, any value of x that is less than or equal to 1.2075 will make the inequality true.

Answer 4

Determine which of the following statements is/are true:

#1: 3⋅20=4(6+9)

#2: 4×12=6×(8×2)12+6⋅64−−√=2⋅4⋅8

#3: 4⋅18−4⋅6=42+4⋅8

Answer 5

Let's evaluate each statement to determine its truth.

#1: 3⋅20 = 4(6+9)
On the left side, we have 3⋅20 = 60. On the right side, 4(6+9) = 4⋅15 = 60. Therefore, statement #1 is true.

#2: 4×12 = 6×(8×2)
On the left side, we have 4×12 = 48. On the right side, 6×(8×2) = 6×16 = 96. Therefore, statement #2 is false.

#3: 4⋅18 − 4⋅6 = 42 + 4⋅8
On the left side, we have 4⋅18 − 4⋅6 = 72 − 24 = 48. On the right side, 42 + 4⋅8 = 42 + 32 = 74. Therefore, statement #3 is false.

In conclusion, statement #1 is true, while statements #2 and #3 are false.