Solve for a

Question

.

1/4(4a+16)=−a+6


(2 points)
a =

Question 2
Now, plug your answer back in to the original equation to check to see if you were right! (1 point)
Responses

I plugged my answer back in to the original equation and it checks out.
I plugged my answer back in to the original equation and it checks out.

I don't know what you mean by plugging my answer in to check.

Answer 1

To solve the equation

\[ \frac{1}{4}(4a + 16) = -a + 6 \]

we start by simplifying the left side:

\[ \frac{1}{4}(4a) + \frac{1}{4}(16) = a + 4 \]

So the equation becomes:

\[ a + 4 = -a + 6 \]

Next, we add \(a\) to both sides:

\[ a + a + 4 = 6 \]

This simplifies to:

\[ 2a + 4 = 6 \]

Now, we subtract 4 from both sides:

\[ 2a = 6 - 4 \]

This gives us:

\[ 2a = 2 \]

Now, we divide both sides by 2:

\[ a = 1 \]

So the solution is:

\[ a = 1 \]

Now, let's check our answer by plugging \(a = 1\) back into the original equation:

The original equation is:

\[ \frac{1}{4}(4a + 16) = -a + 6 \]

Substituting \(a = 1\):

Left side:

\[ \frac{1}{4}(4(1) + 16) = \frac{1}{4}(4 + 16) = \frac{1}{4}(20) = 5 \]

Right side:

\[ -a + 6 = -1 + 6 = 5 \]

Both sides equal 5, so the equation checks out.

Final response:

I plugged my answer back in to the original equation and it checks out.