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)
Isolate the square root term by subtracting 11 from both sides of the equation.
Simplify the equation to get x = 15 − 11 .
Compare the simplified equation 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 need 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
Identifying the Equivalent Equation Now we compare the resulting equation x = 15 − 11 with the given options. The matching equation is x = 15 − 11 .
Final Answer Therefore, the equation equivalent to x + 11 = 15 is x = 15 − 11 .
Examples
Imagine you're trying to figure out how much time you need to prepare for a race. You know that your total training time ( x ) plus the time you spend on other activities (11 hours) equals 15 hours. By finding an equivalent equation, you can easily determine the time you need to dedicate to race training alone. This skill is useful in time management, budgeting, and planning various activities.
The equation equivalent to x + 11 = 15 is x = 15 − 11 , which corresponds to option D. To find this, we isolated the square root by subtracting 11 from both sides. This direct simplification leads us to the answer efficiently.
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