Chapter 3.4, Problem 33STP

To determine

To find: The correct procedure to solve the given system of equations

Answer to Problem 33STP

Option “J” is correct!

Explanation of Solution

Given information: We are given with four options

F

  $\begin{array}{l}-3(x-7)=-16\\ -3x-21=-16\\ -3x=5\\ x=-\frac{5}{3}\end{array}$

H

  $\begin{array}{l}2(x-4)=20\\ 2x-8=20\\ 2x=12\\ x=6\end{array}$

G

  $\begin{array}{l}7-4x=3x+27\\ 7-7x=27\\ -7x=-\frac{20}{7}\\ x=20\end{array}$

J

  $\begin{array}{l}6(2x+1)=30\\ 12x+6=30\\ 12x=24\\ x=2\end{array}$

Calculation:

Check each option

For option F,

  $-3(x-7)=-16$

Distribute the -3 to get rid the ( ).

  $-3x+21=-16$

But the given second step is $-3x-21=-16$ . So, this is incorrect!

For option G,

  $7-4x=3x+27$

Subtract both sides $3x$ and subtract both sides 7

  $-7x=20$

But there it is given $-7x=-\frac{20}{7}$ . So, it is incorrect!

For option H,

  $2(x-4)=20$

Distribute to get rid the parentheses,

  $2x-8=20$

Add both sides 8,

  $2x=28$

But it is given as $2x=12$ . So, it is incorrect!

In option ‘J’ is correct and they solved it correctly!