The equation that matches the same solution as \(3x-5=5x+11\) is \(\boxed{{\mathbf{Option D}}\to{\mathbf{-5=2x+11}}}\) .
Further explanation:
The expression is given as \(3x-5=5x+11\) .
Now, the above expression is simplified as follows:
\(\begin{aligned}3x-5x&=11+5\\-2x&=16\\x&=-\frac{{16}}{2}\\x&=-8\\\end{aligned}\)
Therefore, the value of \(x\) for the given expression is \(-8\) .
Now, the four options are given below.
\(\begin{gathered}{\text{OPTION A}}\to2x-5=11\hfill\\{\text{OPTION B}}\to3x=5x+6\hfill\\{\text{OPTION C}}\to3x+6=5x\hfill\\{\text{OPTION D}}\to-5=2x+11\hfill\\\end{gathered}\)
The simplified form of OPTION A \(2x-5=11\) is given below.
\(\begin{aligned}2x-5&=11\\2x&=11+6\\2x&=17\\x&=\frac{{17}}{2}\\x&=8.5\\\end{aligned}\)
The above solution \(x=8.5\) of the expression \(2x-5=11\) does not match with the obtained solution \(x=-8\) .
Therefore, OPTION A is not the correct answer.
The simplified form of OPTION B \(3x=5x+6\) is given below.
\(\begin{aligned}3x&=5x+6\\3x-5x&=6\\-2x&=6\\x&=-3\\\end{aligned}\)
The above solution \(x=-3\) of the expression \(3x=5x+6\) does not match with the obtained solution \(x=-8\) .
Therefore, OPTION B is not the correct answer.
The simplified form of OPTION C \(3x+6=5x\) is given below.
\(\begin{aligned}3x+6&=5x\\3x-5x&=-6\\-2x&=-6\\x&=3\\\end{aligned}\)
The above solution \(x=3\) of the expression \(3x+6=5x\) does not match with the obtained solution \(x=-8\) .
Therefore, OPTION C is not the correct answer.
The simplified form of OPTION D \(-5=2x+11\) is given below.
\(\begin{aligned}-5&=2x+11\\-5-11&=2x\\-\frac{{16}}{2}&=x\\x&=-8\\\end{aligned}\)
The above solution \(x=-8\) of the expression \(-5=2x+11\) matches with the obtained solution \(x=-8\) .
Therefore, OPTION D is the correct answer.
Thus, the equation that matches the same solution as \(3x-5=5x+11\) is \(\boxed{{\mathbf{Option D}}\to{\mathbf{-5=2x+11}}}\) .
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Answer Details:
Grade: Junior High School
Subject: Mathematics
Chapter: Linear equations
Keywords: expression, equivalent, match, options, \(3x-5=5x+11\) , \(-5x=2x+11\) , equation of line.
