Question

decide whether the equation is an identity, a conditional equation, or a contradiction. give the solution set. - 3(x + 4) + (- 6x) = - 9(x - 4) + 6 a. conditional; {0} b. conditional; {1} c. contradiction; ∅ d. identity; {all real numbers}

Explanation:

Step1: Expand both sides

Left side: $-3(x + 4)+(-6x)=-3x - 12 - 6x=-9x - 12$
Right side: $-9(x - 4)+6=-9x + 36 + 6=-9x + 42$

Step2: Set up the equation

Now we have $-9x - 12=-9x + 42$

Step3: Solve for x

Add $9x$ to both sides: $-12 = 42$ (which is false)

Answer:

C. Contradiction; $\varnothing$