Let's solve the expression step-by-step.
The given expression is:
[tex]\[ 5\sqrt{7} + \sqrt{7} - 2\sqrt{7} \][/tex]
Step 1: Identify the like terms.
The terms [tex]\(5\sqrt{7}\)[/tex], [tex]\(\sqrt{7}\)[/tex], and [tex]\(-2\sqrt{7}\)[/tex] have a common factor, [tex]\(\sqrt{7}\)[/tex].
Step 2: Group the coefficients of like terms.
[tex]\[ 5\sqrt{7} + \sqrt{7} - 2\sqrt{7} = (5 + 1 - 2)\sqrt{7} \][/tex]
Step 3: Perform the arithmetic operations on the coefficients.
[tex]\[ 5 + 1 - 2 = 4 \][/tex]
Step 4: Multiply the result by [tex]\(\sqrt{7}\)[/tex].
[tex]\[ 4\sqrt{7} \][/tex]
Hence, the expression [tex]\(5\sqrt{7} + \sqrt{7} - 2\sqrt{7}\)[/tex] simplifies to [tex]\(4\sqrt{7}\)[/tex].
Thus, the correct answer is:
[tex]\[ 4\sqrt{7} \][/tex]
