Question

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

Answer 1

Let's solve the equation step by step.

The given equation is:

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

First, let's combine like terms on both sides of the equation.

### Step 1: Simplify the left side

On the left side, combine \(\frac{3}{4}x\) and \(-2x\).

To do this, we convert \(-2x\) to a fraction with a common denominator. We can write \(-2x\) as \(-\frac{8}{4}x\):

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

So the left side is now:

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

### Step 2: Simplify the right side

Now, simplify the right side. First combine \(-\frac{1}{4}\) and \(5\):

\[
-\frac{1}{4} + 5 = -\frac{1}{4} + \frac{20}{4} = \frac{19}{4}
\]

Now, combine this with \(\frac{1}{2}x\). Convert \(\frac{1}{2}x\) to have a common denominator with \(\frac{19}{4}\):

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

So the right side becomes:

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

### Step 3: Write the simplified equation

Now we can rewrite the entire equation:

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

### Step 4: Eliminate the fractions

To eliminate the fractions, multiply the whole equation by 4 (the least common denominator):

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

This simplifies to:

\[
-5x + 12 = 2x + 19
\]

### Step 5: Solve for \(x\)

Now, combine like terms:

1. Add \(5x\) to both sides:

\[
12 = 7x + 19
\]

2. Subtract \(19\) from both sides:

\[
12 - 19 = 7x
\]

\[
-7 = 7x
\]

3. Divide both sides by \(7\):

\[
x = -1
\]

So the solution to the equation is:

\[
x = -1
\]