Question

solve the equation 3/4x+3-2x=-1/4+1/2x+5 i combined terms what is the second step?

Answer 1

okay right now i have -5/4x+3=19/4+1/2x add subtract divide or mutiply?

Answer 2

just write it like this as an example:
step 1: combine terms
step 2: add ___
step 3 subtract_
step4: divide this ___

Answer 3

wait how did step 2 said to add 2/4 but there is no 2/4 anywhere?? -5/4x+3=19/4+1/2x

Answer 4

Let's solve the equation step by step. The given equation is:

\[
\frac{3}{4}x + 3 - 2x = -\frac{1}{4} + \frac{1}{2}x + 5
\]

### Step 1: Combine like terms

Let's first combine the constant terms and the x terms on both sides.

**Left side:**

\(\frac{3}{4}x - 2x\) can be written with a common denominator (4):

\[
\frac{3}{4}x - \frac{8}{4}x = -\frac{5}{4}x
\]

So the left side becomes:

\[
-\frac{5}{4}x + 3
\]

**Right side:**

Combine the constants \(-\frac{1}{4} + 5\):

To combine these, you can convert 5 into a fraction with a denominator of 4:

\[
5 = \frac{20}{4}
\]

So,

\[
-\frac{1}{4} + \frac{20}{4} = \frac{19}{4}
\]

Now, you have:

\[
\frac{1}{2}x = \frac{1}{2}x
\]

### The equation now looks like this:

\[
-\frac{5}{4}x + 3 = \frac{1}{2}x + \frac{19}{4}
\]

### Step 2: Isolate the variable

Now, let's isolate the x terms on one side. We can add \(\frac{5}{4}x\) to both sides and subtract \(\frac{19}{4}\) from both sides:

\[
3 - \frac{19}{4} = \frac{1}{2}x + \frac{5}{4}x
\]

Converting 3 into a fraction with a denominator of 4:

\[
3 = \frac{12}{4}
\]

So,

\[
\frac{12}{4} - \frac{19}{4} = \frac{1}{2}x + \frac{5}{4}x
\]

### Step 3: Simplifying both sides

The left side simplifies to:

\[
\frac{12 - 19}{4} = -\frac{7}{4}
\]

On the right side, combine the x terms:

Convert \(\frac{1}{2}x\) into a fraction with a denominator of 4:

\[
\frac{1}{2}x = \frac{2}{4}x
\]

So,

\[
\frac{2}{4}x + \frac{5}{4}x = \frac{7}{4}x
\]

### Step 4: Final equation

Now you have:

\[
-\frac{7}{4} = \frac{7}{4}x
\]

To solve for \(x\), multiply both sides by \(\frac{4}{7}\):

\[
x = -1
\]

And that is the solution!

Answer 5

You have the equation:

\[
-\frac{5}{4}x + 3 = \frac{19}{4} + \frac{1}{2}x
\]

### Step 1: Isolate the variable (x)

To simplify solving the equation, it’s often helpful to isolate \(x\) terms on one side and constants on the other side. Here are the steps to do that:

1. **Move the \(x\) term from the right side to the left side**: Subtract \(\frac{1}{2}x\) from both sides.
2. **Move the constant term from the left side to the right side**: Subtract 3 from both sides.

### Performing the operations:

1. Let's convert \(\frac{1}{2}x\) to a fraction with a denominator of 4 to combine it easily:

\[
\frac{1}{2}x = \frac{2}{4}x
\]

Now subtract \(\frac{2}{4}x\) from both sides:

\[
-\frac{5}{4}x - \frac{2}{4}x + 3 = \frac{19}{4}
\]

This simplifies to:

\[
-\frac{7}{4}x + 3 = \frac{19}{4}
\]

2. Next, subtract 3 (which is \(\frac{12}{4}\)) from both sides:

\[
-\frac{7}{4}x = \frac{19}{4} - \frac{12}{4}
\]

This simplifies to:

\[
-\frac{7}{4}x = \frac{7}{4}
\]

### Step 2: Solve for \(x\)

Now, to solve for \(x\), divide both sides by \(-\frac{7}{4}\):

\[
x = \frac{7/4}{-7/4}
\]

This simplifies to:

\[
x = -1
\]

### Conclusion

To summarize, you added, subtracted, and divided to isolate and solve for \(x\). The answer is:

\[
x = -1
\]

Answer 6

Sure! Here’s a concise step-by-step format for your problem:

**Step 1:** Combine terms.
**Step 2:** Add \(\frac{2}{4}x\) to both sides.
**Step 3:** Subtract 3 (or \(\frac{12}{4}\)) from both sides.
**Step 4:** Divide both sides by \(-\frac{7}{4}\).

This results in:
\[
x = -1
\]

Answer 7

Apologies for any confusion in my previous explanation. Let me clarify that step more accurately based on the equation you provided:

Starting from the equation you have:

\[
-\frac{5}{4}x + 3 = \frac{19}{4} + \frac{1}{2}x
\]

Here's the corrected step-by-step outline:

**Step 1:** Combine terms. (None to combine in this case, we just rearrange the equation)

**Step 2:** Move \(\frac{1}{2}x\) to the left side by subtracting it from both sides:
\[
-\frac{5}{4}x - \frac{1}{2}x + 3 = \frac{19}{4}
\]

(You can express \(\frac{1}{2}x\) as \(\frac{2}{4}x\) for easy subtraction.)

**Step 3:** Move \(3\) to the right side by subtracting \(3\) (or \(\frac{12}{4}\)) from both sides:
\[
-\frac{5}{4}x = \frac{19}{4} - 3
\]

**Step 4:** Calculate \(\frac{19}{4} - \frac{12}{4}\) to simplify the equation:
\[
-\frac{5}{4}x = \frac{7}{4}
\]

**Step 5:** Divide both sides by \(-\frac{5}{4}\):
\[
x = \frac{7/4}{-5/4}
\]

**Step 6:** Simplify to find \(x\):
\[
x = -\frac{7}{5}
\]

### Final Result:
\[
x = -\frac{7}{5}
\]

Thank you for your patience, and I hope this clearer breakdown helps!