Which of the following values of x makes the equation 2x−−√+13=27

Question

true?(1 point)
Responses

49
49

16
16

9
9

25

Answer 1

To solve the equation \( \sqrt{2x} + 13 = 27 \), we can first isolate the square root term.

1. Subtract 13 from both sides: \[ \sqrt{2x} = 27 - 13 \] \[ \sqrt{2x} = 14 \]

2. Next, square both sides to eliminate the square root: \[ 2x = 14^2 \] \[ 2x = 196 \]

3. Divide both sides by 2 to solve for \( x \): \[ x = \frac{196}{2} \] \[ x = 98 \]

Now, let's check which option given in the question (49, 16, 9, 25) satisfies the original equation.

Since none of the provided options are 98, let’s check each of them:

1. For \( x = 49 \): \[ \sqrt{2(49)} + 13 = \sqrt{98} + 13 \approx 9.9 + 13 \neq 27 \]

2. For \( x = 16 \): \[ \sqrt{2(16)} + 13 = \sqrt{32} + 13 \approx 5.7 + 13 \neq 27 \]

3. For \( x = 9 \): \[ \sqrt{2(9)} + 13 = \sqrt{18} + 13 \approx 4.2 + 13 \neq 27 \]

4. For \( x = 25 \): \[ \sqrt{2(25)} + 13 = \sqrt{50} + 13 \approx 7.1 + 13 \neq 27 \]

None of the values \(49, 16, 9, \text{ or } 25\) satisfy the equation.

The original calculation shows that \(x\) should be \(98\) for the equation to be true. Hence, none of the provided answers is correct.