Solve the following equation

Explanation

We will use the distributive property along with the process of combining like terms to simplify the left side of each equation.  It is best to simplify each side of an equation before using a property of equality.

Solution

• This is the equation to solve
  • 3(k + 1) - 5k = 0
• Distribute the multiplication by 3
  • 3k + 3 - 5k = 0
• Combine like terms: 3k - 5k = -2k.  First, we want to isolate the variable term, -2k
  • -2 + 3 = 0
• To undo the addition of 3, subtract 3 from both sides.  This isolates -2k
  • -2k + 3 -3 = 0 - 3
• Do the subtractions: 3 - 3 = 0 and 0 - 3 = -3.  Now we want to isolate the variable, k
  • -2k = -3
• To undo the multiplication by -2, divide both sides by -2.  This isolates k.
  • \(\frac{-2k}{-2} = \frac{-3}{-2}\)
• On the right side, simplify: \(\frac{-3}{-2} = \frac{3}{2}\)
  • k = \(\frac32\)

Check the solution by substituting in the original equation