What is the smallest integer that satisfies the inequality 2x - 5 > -11?

What is the smallest integer that satisfies the inequality 2x - 5 > -11?

• A. -3
• B. -2
• C. -1
• D. 0

Answer: (B)

To solve the inequality \(2x - 5 > -11\), we start by isolating \(x\). First, we can add 5 to both sides of the inequality: \[ 2x - 5 + 5 > -11 + 5 \] This simplifies to: \[ 2x > -6 \] Next, we divide both sides by 2 to solve for \(x\): \[ x > -3 \] This tells us that \(x\) must be greater than \(-3\). The smallest integer that meets this criterion is \(-2\), making it the correct answer. To verify, we can check that \(-2\) is indeed greater than \(-3\). Any integer less than or equal to \(-3\) would not satisfy the inequality, hence they do not qualify as solutions. Therefore, \(-2\) is the smallest integer that satisfies the inequality \(2x - 5 > -11\).

To solve the inequality (2x - 5 > -11), we start by isolating (x).

First, we can add 5 to both sides of the inequality:

[

2x - 5 + 5 > -11 + 5

]

This simplifies to:

[

2x > -6

]

Next, we divide both sides by 2 to solve for (x):

[

x > -3

]

This tells us that (x) must be greater than (-3). The smallest integer that meets this criterion is (-2), making it the correct answer.

To verify, we can check that (-2) is indeed greater than (-3). Any integer less than or equal to (-3) would not satisfy the inequality, hence they do not qualify as solutions. Therefore, (-2) is the smallest integer that satisfies the inequality (2x - 5 > -11).