To find an equivalent equation to [tex]\(\sqrt{x} + 11 = 15\)[/tex], we need to isolate the square root term, [tex]\(\sqrt{x}\)[/tex]. Here is a step-by-step guide:
1. Start with the original equation:
[tex]\[
\sqrt{x} + 11 = 15
\][/tex]
2. To isolate [tex]\(\sqrt{x}\)[/tex], subtract 11 from both sides of the equation:
[tex]\[
\sqrt{x} + 11 - 11 = 15 - 11
\][/tex]
3. Simplify both sides:
[tex]\[
\sqrt{x} = 4
\][/tex]
Therefore, the equivalent equation for [tex]\(\sqrt{x} + 11 = 15\)[/tex] is [tex]\(\sqrt{x} = 4\)[/tex].
Now, let's look at the given options:
1. [tex]\(x + 11 = 225\)[/tex]
2. [tex]\(x + 121 = 225\)[/tex]
3. [tex]\(\sqrt{x} - 15 + 11\)[/tex]
4. [tex]\(\sqrt{x} = 15 - 7\)[/tex]
Comparing these with [tex]\(\sqrt{x} = 4\)[/tex]:
- [tex]\(x + 11 = 225\)[/tex]: This is incorrect.
- [tex]\(x + 121 = 225\)[/tex]: This is incorrect.
- [tex]\(\sqrt{x} - 15 + 11\)[/tex]: This simplifies to [tex]\(\sqrt{x} - 4\)[/tex], which is not equivalent.
- [tex]\(\sqrt{x} = 15 - 7\)[/tex]: This simplifies to [tex]\(\sqrt{x} = 8\)[/tex], which is not correct.
None of the provided options match exactly [tex]\(\sqrt{x} = 4\)[/tex]. But if we manipulate option 4 [tex]\(\sqrt{x} = 15 - 7\)[/tex], we can simplify it:
1. Simplify the right-hand side:
[tex]\[
\sqrt{x} = 8
\][/tex]
Thus, although the correct equation [tex]\(\sqrt{x} = 4\)[/tex] isn’t explicitly listed, if the problem and choices have been transcribed correctly, and option 4 simplifies to [tex]\(\sqrt{x} = 8\)[/tex]—it might suggest there was a mistake in the provided options.
Therefore, the equivalent equation to [tex]\(\sqrt{x} + 11 = 15\)[/tex] should be:
[tex]\[
\sqrt{x} = 4
\][/tex]
