Chapter 8.7, Problem 59STP

To determine

To find:The correct equation whose solution is $-2$ .

Answer to Problem 59STP

The correct option is (H)

Explanation of Solution

Given Information:The given equationsare $x+3=2x+1$ , $x-5=2x-7$ , $2x+5=5x+11$ , $3x+1=x-5$

Concept used:

Substitute the value $x=-2$ . If both the sides are equal, then $x=-2$ is the solution.

Calculation:

For the first equation $x+3=2x+1$

Take left-hand side and proceed.

  $\begin{array}{c}x+3=-2+3\\ =1\end{array}$

Take the right-hand side and proceed.

  $\begin{array}{c}2x+1=2\left(-2\right)+1\\ =-4+1\\ =-3\end{array}$

The values on both the sides are not same.

Therefore, $-2$ is not the solution of the equation $x+3=2x+1$

For the second equation $x-5=2x-7$

Take left-hand side and proceed.

  $\begin{array}{c}x-5=-2-5\\ =-7\end{array}$

Take the right-hand side and proceed.

  $\begin{array}{c}2x-7=2\left(-2\right)-7\\ =-4-7\\ =-11\end{array}$

The values on both the sides are not same.

Therefore, $-2$ is not the solution of the equation $x-5=2x-7$

For the third equation $2x+5=5x+11$

Take left-hand side and proceed.

  $\begin{array}{c}2x+5=2\left(-2\right)+5\\ =-4+5\\ =1\end{array}$

Take the right-hand side and proceed.

  $\begin{array}{c}5x+11=5\left(-2\right)+11\\ =-10+11\\ =1\end{array}$

The values on both the sides are same.

Therefore, $-2$ is the solution of the equation $2x+5=5x+11$

For the fourth equation $3x+1=x-5$

Take left-hand side and proceed.

  $\begin{array}{c}3x+1=3\left(-2\right)+1\\ =-6+1\\ =-5\end{array}$

Take the right-hand side and proceed.

  $\begin{array}{c}x-5=\left(-2\right)-5\\ =-7\end{array}$

The values on both the sides are not same.

Therefore, $-2$ is not the solution of the equation $3x+1=x-5$