Chapter 1.8, Problem 2STP

For Exercises $1-5,$ choose the correct letter.

Which equation has a solution of $-6?$

F. $15x-20=70$

G. $14=6x-22$

H. $3x-8=-10$

I. $\frac{1}{2}x-8=-11$

To determine

To find: The equation which gives the solution of -6.

Answer to Problem 2STP

The equation which gives the solution -6 is $\frac{1}{2}x-8=-11$ .

Explanation of Solution

Given information: A solution to an equation given -6. Four options given, $F.15x-20=70$ , $G.14=6x-22$ , $H.3x-8=-10$ , $I.\frac{1}{2}x-8=-11$ .

Calculation:

By solving the equation in option F,

$\begin{array}{l}15x-20=70\\ \Rightarrow 15x=70+20\\ \Rightarrow 15x=90\\ \Rightarrow x=\frac{90}{15}\\ \therefore x=6\end{array}$

By solving the equation in option G,

$\begin{array}{l}14=6x-22\\ \Rightarrow 14+22=6x\\ \Rightarrow 36=6x\\ \Rightarrow 6x=36\\ \Rightarrow x=\frac{36}{6}\\ \therefore x=6\end{array}$

By solving the equation in option H,

$\begin{array}{l}3x-8=-10\\ \Rightarrow 3x=-10+8\\ \Rightarrow 3x=-2\\ \Rightarrow x=-\frac{2}{3}\end{array}$

By solving the equation in option I,

$\begin{array}{l}\frac{1}{2}x-8=-11\\ \Rightarrow \frac{1}{2}x=-11+8\\ \Rightarrow \frac{1}{2}x=-3\\ \Rightarrow x=-3\times 2\\ \therefore x=-6\end{array}$

  $\therefore$ The solution -6 is for the equation in option I.