Question

Which of the following equations has the same solution as 3x-5=5x+11?

Answer 1

3x-5=5x+11

subtract 3x to both sides

3x-5 - 3x =5x+11 - 3x

simplify
-5 = 2x +11

answer is D. -5=2x+11

Answer 2

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 $\boxed{{\mathbf{Option D}}\to{\mathbf{-5=2x+11}}}$ .

Learn more:

1. Which expression is equivalent to ? brainly.com/question/3658196

2. What are the values of x? brainly.com/question/2093003

3. Which expression is a sum of cubes? brainly.com/question/4102355

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.