To find the solution(s) to the equation [tex]\(4x = -4x\)[/tex], let's solve it step-by-step:
1. First, combine like terms:
[tex]\[ 4x + 4x = 0 \][/tex]
2. Simplify the equation:
[tex]\[ 8x = 0 \][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[ x = 0 \][/tex]
So, the only solution to the equation [tex]\(4x = -4x\)[/tex] is [tex]\(x = 0\)[/tex].
To visualize this solution on a graph, consider the equations of two lines derived from the given equality:
1. Equation 1:
[tex]\[ y = 4x \][/tex]
2. Equation 2:
[tex]\[ y = -4x \][/tex]
These are two linear equations that represent straight lines on the coordinate plane. Let's describe how to plot these graphs:
### Plotting the Graphs:
1. Draw the coordinate axes:
- Draw a horizontal axis ([tex]\(x\)[/tex]-axis) and a vertical axis ([tex]\(y\)[/tex]-axis).
- Mark appropriate scales on both axes.
2. Plot [tex]\(y = 4x\)[/tex]:
- This line has a slope of 4, meaning it rises 4 units for every 1 unit it moves to the right.
- To plot it, you can use the origin [tex]\((0,0)\)[/tex] and another point like [tex]\((1,4)\)[/tex].
- Connect these points with a straight line.
3. Plot [tex]\(y = -4x\)[/tex]:
- This line has a slope of -4, meaning it falls 4 units for every 1 unit it moves to the right.
- Again, use the origin [tex]\((0,0)\)[/tex] and another point like [tex]\((1,-4)\)[/tex].
- Connect these points with a straight line.
### Intersection Point:
- The lines [tex]\(y = 4x\)[/tex] and [tex]\(y = -4x\)[/tex] intersect at the origin [tex]\((0,0)\)[/tex].
Therefore, by plotting the graphs of [tex]\(y = 4x\)[/tex] and [tex]\(y = -4x\)[/tex], you can see that they intersect exactly at [tex]\(x = 0\)[/tex]. This visual representation confirms that the solution to the equation [tex]\(4x = -4x\)[/tex] is [tex]\(x = 0\)[/tex].
