Question

Fill in the spaces to solve each step of the problem 1/4(x+3)=5
.(2 points)
Step 1: (_)14(x+3)=5(_).
Step 2: x+3=__

Step 3: Subtract __ from both sides.
Step 4: x= __

fill in the blanks __

Answer 1

why is it in step one it isnt divide by 1/4? why is just 4? explain

Answer 2

alr thank you!

Answer 3

Let's solve the equation step by step and fill in the blanks.

The original equation is:
\[
\frac{1}{4}(x+3)=5.
\]

**Step 1**: Multiply both sides by 4 to eliminate the fraction:
\[
(4)\cdot\frac{1}{4}(x+3) = 5(4).
\]
This simplifies to:
\[
1(x+3) = 20.
\]
So in this step, you can fill in the blanks as follows:
\[
(4)14(x+3)=5(4).
\]

**Step 2**: From \(1(x+3) = 20\), we can simplify to:
\[
x+3=20.
\]

**Step 3**: Subtract 3 from both sides:
\[
x + 3 - 3 = 20 - 3.
\]
So we fill in the blank:
\[
\text{Subtract } 3 \text{ from both sides}.
\]

**Step 4**: This gives us:
\[
x = 17.
\]

Putting it all together, the filled-in blanks would be:
1. (4)14(x+3)=5(4).
2. x+3=20.
3. Subtract 3 from both sides.
4. x=17.

Answer 4

That's a great question! The process of solving the equation by multiplying both sides by \(4\) instead of dividing by \(\frac{1}{4}\) is indeed related. Here’s the step-by-step explanation:

When you have the equation:

\[
\frac{1}{4}(x + 3) = 5,
\]

you want to get rid of the fraction to make the equation easier to solve. Dividing by \(\frac{1}{4}\) is mathematically correct, but it can be a bit less straightforward for some people.

### Why Multiply by 4?

To eliminate the \(\frac{1}{4}\), you can multiply both sides of the equation by the reciprocal of \(\frac{1}{4}\), which is \(4\).

Here's how that looks:

1. **Multiply Both Sides by 4**:

\[
4 \times \frac{1}{4}(x + 3) = 4 \times 5.
\]

On the left-hand side, multiplying by \(4\) cancels \(\frac{1}{4}\):

\[
1(x + 3) = 20.
\]

This is because:

\[
4 \cdot \frac{1}{4} = 1.
\]

2. **Result**:

Now you are left with:

\[
x + 3 = 20.
\]

### Why Not Divide by \(\frac{1}{4}\)?

If you were to divide by \(\frac{1}{4}\), you would actually be multiplying by \(4\) (because dividing by a fraction is the same as multiplying by its reciprocal). Here’s how that looks mathematically:

\[
\frac{1}{4}(x + 3) = 5 \quad \Rightarrow \quad (x + 3) = 5 \div \frac{1}{4} = 5 \times 4 = 20.
\]

In both methods—multiplying by \(4\) or dividing by \(\frac{1}{4}\)—you arrive at the same equation, \(x + 3 = 20\). So, choosing to multiply by \(4\) is often simpler and more direct, especially when teaching or explaining the concept.

In summary, multiplying by \(4\) is just a straightforward alternative that achieves the same goal in a more intuitive and simpler way.

Answer 5

You're welcome! I'm glad I could help. If you have any more questions or if there's anything else you'd like to know, feel free to ask!