To solve the equation \( -52x - 1 = 4x + 2 \), let's start by isolating the variable \( x \).
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Get all terms with \( x \) on one side:
Add \( 52x \) to both sides: \[ -1 = 4x + 52x + 2 \] This simplifies to: \[ -1 = 56x + 2 \]
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Combine like terms:
Subtract \( 2 \) from both sides: \[ -1 - 2 = 56x \] So, \[ -3 = 56x \]
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Solve for \( x \):
Divide both sides by \( 56 \): \[ x = \frac{-3}{56} \]
Now that we have \( x = \frac{-3}{56} \), you'll want to find the graph that intersects the line \( y = -52x - 1 \) and \( y = 4x + 2 \) at this point.
To visually represent \( x = \frac{-3}{56} \):
- You can check the values for \( x \) in both equations to see the exact coordinates.
For plotting, substitute \( x = -\frac{3}{56} \) into both equations to find the corresponding \( y \)-values.
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For \( y = -52x - 1 \): \[ y = -52\left(-\frac{3}{56}\right) - 1 = \frac{156}{56} - 1 = \frac{156}{56} - \frac{56}{56} = \frac{100}{56} \]
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For \( y = 4x + 2 \): \[ y = 4\left(-\frac{3}{56}\right) + 2 = -\frac{12}{56} + 2 = -\frac{12}{56} + \frac{112}{56} = \frac{100}{56} \]
Both methods give the point \( \left(-\frac{3}{56}, \frac{100}{56}\right) \).
Check for the graph with the intersection at \( \left(-\frac{3}{56}, \frac{100}{56}\right) \). The correct graph representation should show this point clearly on the plots of the two equations.
If you have specific graphs to evaluate, please analyze based on the intersection point calculated.
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