Solving Linear Equations with Fractions Quiz

Study Notes

To solve the equation (\frac{2}{3}x + 4 = 6), isolate (x):
- Subtract 4 from both sides: (\frac{2}{3}x = 2)
- Multiply both sides by (\frac{3}{2}): (x = 3)
For the equation (\frac{5}{2} - x = \frac{1}{4}), solve for (x):
- Rearrange to find (x): (x = \frac{5}{2} - \frac{1}{4})
- Convert (\frac{5}{2}) to (\frac{10}{4}): (x = \frac{10}{4} - \frac{1}{4} = \frac{9}{4})
In the equation (\frac{x}{4} + \frac{x}{3} = 5), find (x):
- Find a common denominator (12): (\frac{3x}{12} + \frac{4x}{12} = 5)
- Combine terms: (\frac{7x}{12} = 5)
- Multiply by 12 and divide by 7: (x = \frac{60}{7})
To solve for (x) in (3x - 7 = 5x + 3):
- Rearrange terms: (3x - 5x = 3 + 7)
- Simplify to (-2x = 10)
- Divide by -2: (x = -5)
The equation (\frac{2}{5}x - 3 = \frac{1}{4}x + 12) requires isolating (x):
- Rearrange to get all (x) terms on one side and constants on the other.
- Multiply through to eliminate fractions if necessary.
To find (x) in (\frac{3}{2}x + 5 = \frac{1}{4}x - 3):
- Isolate terms and convert fractions as needed to combine like terms.

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