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Which value of x is a solution of the inequality?

​ 3x+5≤14 ​

Responses

x = 3
x = 3

x = 4
x = 4

x = 5
x = 5

x = 6

1 answer

To solve the inequality \( 3x + 5 \leq 14 \), we will isolate \( x \).

  1. Subtract 5 from both sides: \[ 3x + 5 - 5 \leq 14 - 5 \] which simplifies to: \[ 3x \leq 9 \]

  2. Next, divide both sides by 3: \[ \frac{3x}{3} \leq \frac{9}{3} \] which gives: \[ x \leq 3 \]

Now, we are looking for valid values of \( x \) that satisfy the inequality \( x \leq 3 \).

Among the provided responses:

  • \( x = 3 \) is a solution since \( 3 \leq 3 \).
  • \( x = 4 \) is not a solution since \( 4 > 3 \).
  • \( x = 5 \) is not a solution since \( 5 > 3 \).
  • \( x = 6 \) is not a solution since \( 6 > 3 \).

Therefore, the correct answer is: x = 3.