Solving Linear Equations with Fractions Quiz

Algebraic Equations and Solutions

• 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.

Computer System Components

• A monitor is an output device that displays visual information from the computer.

• The device responsible for converting input into digital data is often referred to as an input device, such as a keyboard or a mouse.

• The primary function of a printer is to produce hard copies of digital documents or images, converting digital data back into a physical format.