Question

Which equation, when solved results in a different value of x than the other three?

Answer 1

Answer:

$-\frac{7}{8}(-\frac{8}{7})x-\frac{3}{4}=20(-\frac{8}{7})$

Step-by-step explanation:

The complete question in the attached figure

Verify each case

Part 1) we have

$-\frac{7}{8}x-\frac{3}{4}=20$

solve for x

$\frac{7}{8}x=-\frac{3}{4}-20$

$\frac{7}{8}x=-\frac{83}{4}$

$x=-\frac{83}{4}(\frac{8}{7})$

$x=-\frac{166}{7}$

Part 2) we have

$\frac{3}{4}+\frac{7}{8}x=-20$

Multiply both sides by -1 and rearrange the terms on the left side to get

$-\frac{7}{8}x-\frac{3}{4}=20$

This expression is the same that the expression in Part 1)

That means, that the equations Part 1) and Part 2) are equivalent

therefore

$x=-\frac{166}{7}$

Part 3) we have

$-7(\frac{1}{8})x-\frac{3}{4}=20$

Remember that

$-7(\frac{1}{8})x=-\frac{7}{8}x$

This expression is the same that the expression in Part 1)

That means, that the equations Part 1) and Part 3) are equivalent

therefore

$x=-\frac{166}{7}$

Part 4) we have

$-\frac{7}{8}(-\frac{8}{7})x-\frac{3}{4}=20(-\frac{8}{7})$

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