Which equation is equivalent to $\sqrt{x}+11=15 ?$
A. $x+11=225$
B. $x+121=225$
C. $\sqrt{x}=15+11$
D. $\sqrt{x}=15-11$
Answer (2)
Start with the given equation: x + 11 = 15 .
Isolate the square root term by subtracting 11 from both sides: x = 15 − 11 .
Compare the result with the given options.
The equivalent equation is x = 15 − 11 .
Explanation
Understanding the Problem We are given the equation x + 11 = 15 and asked to find an equivalent equation from the given options.
Isolating the Square Root To find an equivalent equation, we want to isolate the square root term. We can do this by subtracting 11 from both sides of the equation: x + 11 − 11 = 15 − 11 x = 15 − 11
Finding the Equivalent Equation Now we compare the resulting equation, x = 15 − 11 , with the given options. We see that it matches one of the options.
Final Answer Therefore, the equivalent equation is x = 15 − 11 .
Examples
In real life, this type of problem can be used when working with distances and velocities. For example, if the velocity of an object is related to the square root of the distance it travels, and you know the velocity plus a constant, you can use this type of equation to find the distance traveled.
The equivalent equation to x + 11 = 15 is x = 15 − 11 , which corresponds to option D. Therefore, the correct answer is D.
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