Question

15. Higher Order Thinking The equation shownhas a missing value.-2(2x - 1) + 1 = 17 - 4xa. For what missing value is the equation anidentity?b. For what missing value(s), if any, does theequation have exactly one solution?C. For what missing value(s), if any, does theequation have no solution?

Answer 1

we have the following:

$-2\left(2x-\text{ }\right)+1=17-4x$

a. For what missing value is the equation an identity?

Is an identity when both sides are equal.

$\begin{gathered} -2\left(2x-8\right)+1=17-4x \\ -4x+16+1=17-4x \\ 17-4x=17-4x \end{gathered}$

therefore, the answer is 8.

b. For what missing value(s), if any, does the equation have exactly one solution?

The equation has exactly one solution for missing value = 8

$\begin{gathered} -2\left(2x-8\right)+1=17-4x \\ -4x+16+1=17-4x \\ 17-4x=17-4x \end{gathered}$

therefore, the answer is 8.

c. For what missing value(s), if any, does the equation have no solution?

The equation has no solution when the leff and right hand side of the equation must be unequal.

therefore, the answer can have any value except 8