Solve the following equation

Explanation

First we will use a property of equality to isolate the variable term on one side of the equation. Then we will use a second property of equality to isolate the variable itself.  To solve the original equation, we want to find a simpler equivalent equation of the form x = a number, whose solution is obvious.

Solution

On the left side of the equation, x is multiplied by 12, and then 5 is added to that product.  To isolate x, we undo the operations in the opposite order.

• To isolate the variable term, 12x, we subtract 5 from both sides to undo the addition of 5.
• To isolate the variable, x, we divide both sides by 12 to undo the multiplication by 12.

• This is the equation to solve.  First, we want to isolate the variable term, 12x
  • 12x + 5 = 17
• Use the subtraction property of equality:  Subtract 5 from both sides to isolate 12x
  • 12x + 5 - 5 = 17 - 5
• Do the subtraction: 5 - 5 = 0 and 17 - 5 = 12.  Now we want to isolate the variable, x
  • 12x = 12
• Use the division property of equality: Divide both sides by 12 to isolate x
  • \(\frac{12x}{12} = \frac{12}{12}\)
• On the left side simplify: \(\require{cancel} \frac{\cancel{12}^1}{\cancel{12}_1} = x\)
  • x = 1

Check

• This is the original equation
  • 12x + 5 = 17
• Substitute 1 for x
  • 12(1) + 5 = 17
• Do the multiplication on the left side
  • 12 + 5 = 17
• True
  • 17 = 17

The solution is 1