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