Question

decide whether the given equation is an identity, a conditional equation, or a contradiction. give the solution set 0.3(x + 2)-0.6(x + 2)=-0.3x - 0.6 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. x = (simplify your answer.) b. the solution is all real numbers. c. there is no solution.

Explanation:

Step1: Expand the left - hand side

\[

$$\begin{align*} 0.3(x + 2)-0.6(x + 2)&=(0.3x+0.6)-(0.6x + 1.2)\\ &=0.3x+0.6 - 0.6x-1.2\\ &=(0.3x-0.6x)+(0.6 - 1.2)\\ &=- 0.3x-0.6 \end{align*}$$

\]

Step2: Compare with the right - hand side

The left - hand side $0.3(x + 2)-0.6(x + 2)=-0.3x - 0.6$ is equal to the right - hand side $-0.3x-0.6$ for all real values of $x$.

Answer:

B. The solution is all real numbers.