Question

Which graph represents the solution for the equation −5/2x−1=4x+2
?(1 point)

Answer 1

To solve the equation \(-\frac{5}{2}x - 1 = 4x + 2\), we can follow these steps:

1. **Eliminate the fractions**: Multiply the entire equation by 2 to get rid of the fraction:
\[
2 \left(-\frac{5}{2}x - 1\right) = 2(4x + 2)
\]
This simplifies to:
\[
-5x - 2 = 8x + 4
\]

2. **Rearrange the equation**: Add \(5x\) to both sides:
\[
-2 = 8x + 5x + 4
\]
This simplifies to:
\[
-2 = 13x + 4
\]

3. **Isolate \(x\)**: Subtract 4 from both sides:
\[
-2 - 4 = 13x
\]
This gives:
\[
-6 = 13x
\]

4. **Solve for \(x\)**: Divide both sides by 13:
\[
x = -\frac{6}{13}
\]

Now that we have \(x = -\frac{6}{13}\), you can use this value to plot the solution on a graph.

To identify which graph represents the solution, look for the one that shows a point or a line crossing the x-axis at \(x = -\frac{6}{13}\) or equivalently around \(-0.46\) on the x-axis.

If this is a multiple-choice question, you'd want to select the graph that reflects that point. If there are further options or details about the specific graphs, please provide those for more guidance!