Question

The solution to -6(2-2) = 36 - 10z isA-6B 1.5C 1206PARTBWhat is the solution for the equation 64c - 16 = 16(4c - 1)?-1В) 0c) all real numbersD no solution

Answer 1

PART A: D) 6

PART B: C) all real numbers

Step-by-step explanation

PART A

First we have to apply the distributive property for the -6 in the left term:

`\begin{gathered} -6(x-2)=36-10x \\ -6x+12=36-10x \end{gathered}`

Now we have to put all the terms that contain x on the same side. Add 10x on both sides:

`\begin{gathered} -6x+10x+12=36-10x+10x \\ 4x+12=36 \end{gathered}`

Leave just the term with x on the left term: subtract 12 from both sides:

`\begin{gathered} 4x+12-12=36-12 \\ 4x=24 \end{gathered}`

And finally divide both sides by 4:

`\begin{gathered} (4x)/(4)=(24)/(4) \\ x=6 \end{gathered}`

PART B

The process for this equation is similar. First we apply the distributive property on the right side:

`\begin{gathered} 64c-16=16\cdot4c-16\cdot1 \\ 64c-16=64c-16 \end{gathered}`

Note that both sides of the equation are the same. This means that any value for c will make this equation true and hence, the solution is all real numbers