Vanessa tried to solve an equation step by step. \qquad\begin{aligned} -12&=4(f-6) \\ -12&=4f-24&\green{\text{Ste p } 1} \\ 12&=4f&\blue{\text{Step } 2} \\ 4&=f&\purple{\text{Step } 3} \end{aligned} −12 −12 12 4 =4(f−6) =4f−24 =4f =f Step 1 Step 2 Step 3 Find Vanessa's mistake

STEP 3: f=4

Step-by-step explanation:

Given the steps to the solution of the given equation:

Given Steps 1 to 3 above, Vanessa wrongly calculated the division of 12 by 4 as 4 in Step 3.

Corrected, this becomes:

Therefore, f=3

d is correct

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.