Solve the following equation

Explanation

We will use the distributive property of each side of the equation to remove the parentheses.  Then we will combine any like terms.  It is easiest to simplify the expressions that make up the left and right sides of the equation before using the properties of equality to isolate the variable.

Solution

• This is the equation to solve
  • 3(4x - 80) + 6x = 2(x + 40)
• Distribute the multiplication by 3 and by 2
  • 12x - 240 + 6x = 2x + 80
• On the left side, combine like terms:  12x + 6x = 18x.  There are variable terms on both sides.
  • 18x - 240 = 2x + 80
• To eliminate the term 2x on the right side, subtract 2x from both sides.
  • 18x - 240 - 2x = 2x + 80 -2x
• Combine like terms on each side: 18x - 2x  = 16x and 2x -2x = 0
  • 16x - 240 = 80
• To isolate the variable term, 16x, on the left side, add 240 to both sides to undo the subtraction of 240
  • 16x - 240 + 240 = 80 + 240
• Do the addition on each side: -240 + 240 = 0 and 80 + 240 = 320.  Now we want to isolate the variable, x
  • 16x = 320
• To isolate x on the left side, divide both sides by 16 to undo the multiplication by 16
  • \(\frac{16x}{16} = \frac{320}{16}\)
• On the left side, simplify, \(\require{cancel} \frac{\cancel{16}^1x}{\cancel{16}_1} = x\).  On the right side, do the division.
  • x = 20

The solution is 20.  Check by substituting in the original equation.