Question

Is the equation
−2(4−x)=2x+8
−2(4−x)=2x+8
an identity? Explain your reasoning.


Yes, because solving the equation gives a statement that is never true.

Yes, because solving the equation gives a statement that is always true.

No, because solving the equation gives a statement that is never true.

No, because solving the equation gives a statement that is always true.

Answer 1

Answer on Question #80111 – Math – Algebra

Question

Is the equation $-2(4-x)=2x+8$ an identity? Explain your reasoning.

Solution

An identity equation is an equation that is always true for any value substituted into the variable.

We consider the equation $-2(4-x)=2x+8$

Let us open the brackets on the left side of equation:

$$-2(4-x) = -8 + 2x$$

As a result, the initial equation takes the form:

$$-8 + 2x = 2x + 8$$

After collecting all the terms of the equation in the left side we get:

$$\begin{array}{l} -8 + 2x - 2x - 8 = 0 \\ -16 = 0 \\ \end{array}$$

This statement is false for every value of $x$. Therefore, the equation is not an identity.

Answer: No, because solving the equation gives a statement that is never true.

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