If 2x + 5 andgt; 2 + 3x and 2x - 3 andle; 4x - 5, then x can take which of the following values?a)-2b)2c)4d)-4Correct answer is option 'B'. Can you explain this answer?

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ACT Exam > ACT Questions > If 2x + 5 > 2 + 3x and 2x - 3 ≤ 4x - 5,...

If 2x + 5 > 2 + 3x and 2x - 3 ≤ 4x - 5, then x can take which of the following values?

a)
-2
b)
2
c)
4
d)
-4

Correct answer is option 'B'. Can you explain this answer?

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If 2x + 5 > 2 + 3x and 2x - 3 ≤ 4x - 5, then x can take which of...

2x + 5 > 2 + 3x

5 – 2 > 3x – 2x

3 > x .......(1)

2x - 3 ≤ 4x - 5

5 – 3 ≤ 4x – 2x

1 ≤ x .......(2)

From (1) and (2)

x = 1 or 2

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Most Upvoted Answer

If 2x + 5 > 2 + 3x and 2x - 3 ≤ 4x - 5, then x can take which of...

Given Inequalities:
2x + 5 > 2 + 3x
2x - 3 ≤ 4x - 5

Solving the first inequality:
2x + 5 > 2 + 3x
5 - 2 > 3x - 2x
3 > x

Solving the second inequality:
2x - 3 ≤ 4x - 5
-3 + 5 ≤ 4x - 2x
2 ≤ 2x
1 ≤ x

Combining the solutions:
Since x must satisfy both inequalities, x must be greater than 1 (from the second inequality) and less than 3 (from the first inequality). Therefore, x can take the value of 2.

Correct Answer:
Therefore, option B) 2 is the correct value for x based on the given inequalities.

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If 2x + 5 > 2 + 3x and 2x - 3 ≤ 4x - 5, then x can take which of...

2x + 5 > 2 + 3x

5 – 2 > 3x – 2x

3 > x .......(1)

2x - 3 ≤ 4x - 5

5 – 3 ≤ 4x – 2x

1 ≤ x .......(2)

From (1) and (2)

x = 1 or 2

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If 2x + 5 > 2 + 3x and 2x - 3 ≤ 4x - 5, then x can take which of the following values?a)-2b)2c)4d)-4Correct answer is option 'B'. Can you explain this answer?

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