Question

solve and check the linear equation.
\\((x - 2) - 2(x - 1) = x + 1 - (x - 2)\\)
what is the solution? select the correct choice below and, if necessary, fill in the answer box to complete your ch
\\(\bigcirc\\) a. the solution set is \\(\\{\\ \\}\\).
\\(\bigcirc\\) b. the solution set is \\(\\{x \mid x\text{ is a real number}\\}\\).
\\(\bigcirc\\) c. the solution set is \\(\varnothing\\).

Explanation:

Step1: Expand both sides

Left side: $(x-2)-2(x-1) = x - 2 - 2x + 2$
Right side: $x+1-(x-2) = x + 1 - x + 2$

Step2: Simplify both sides

Left side: $x - 2 - 2x + 2 = -x$
Right side: $x + 1 - x + 2 = 3$

Step3: Solve for $x$

$-x = 3$
Multiply both sides by $-1$: $x = -3$

Step4: Verify the solution

Substitute $x=-3$ into original equation:
Left: $(-3-2)-2(-3-1) = -5 - 2(-4) = -5 + 8 = 3$
Right: $-3+1-(-3-2) = -2 - (-5) = -2 + 5 = 3$
Both sides are equal, so $x=-3$ is valid.

Answer:

A. The solution set is $\{-3\}$