Answer:
[tex]-\frac{7}{8}(-\frac{8}{7})x-\frac{3}{4}=20(-\frac{8}{7})[/tex]
Step-by-step explanation:
The complete question in the attached figure
Verify each case
Part 1) we have
[tex]-\frac{7}{8}x-\frac{3}{4}=20[/tex]
solve for x
[tex]\frac{7}{8}x=-\frac{3}{4}-20[/tex]
[tex]\frac{7}{8}x=-\frac{83}{4}[/tex]
[tex]x=-\frac{83}{4}(\frac{8}{7})[/tex]
[tex]x=-\frac{166}{7}[/tex]
Part 2) we have
[tex]\frac{3}{4}+\frac{7}{8}x=-20[/tex]
Multiply both sides by -1 and rearrange the terms on the left side to get
[tex]-\frac{7}{8}x-\frac{3}{4}=20[/tex]
This expression is the same that the expression in Part 1)
That means, that the equations Part 1) and Part 2) are equivalent
therefore
[tex]x=-\frac{166}{7}[/tex]
Part 3) we have
[tex]-7(\frac{1}{8})x-\frac{3}{4}=20[/tex]
Remember that
[tex]-7(\frac{1}{8})x=-\frac{7}{8}x[/tex]
This expression is the same that the expression in Part 1)
That means, that the equations Part 1) and Part 3) are equivalent
therefore
[tex]x=-\frac{166}{7}[/tex]
Part 4) we have
[tex]-\frac{7}{8}(-\frac{8}{7})x-\frac{3}{4}=20(-\frac{8}{7})[/tex]
This equation is not equivalent to the other three, because some terms are multiplied by -8/7 and others are not. When different things are done on either side of the equal sign, it changes the equation, resulting in a different solution
