Write and solve the equation and then check your answer. Select the correct statements for each blank. A number decreased by sixty-eight is thirty-one. (5 points) Equation: This is a problem. To solve the equation, to both sides of the equation. To check the solution, 99 for the variable in the equation.

1 answer

Let's break down the problem step-by-step:

  1. Understanding the problem: A number decreased by sixty-eight is thirty-one means we can express this as an equation. Let the number be represented by \( x \). The equation becomes: \[ x - 68 = 31 \]

  2. Solving the equation: To solve for \( x \), we need to isolate \( x \) on one side. We can do this by adding 68 to both sides of the equation: \[ x - 68 + 68 = 31 + 68 \] Simplifying this gives us: \[ x = 99 \]

  3. Checking the solution: We can check our solution by substituting \( x = 99 \) back into the original equation: \[ 99 - 68 = 31 \] This simplifies to: \[ 31 = 31 \] which is true, confirming that our solution is correct.

Now, let's fill in the blanks based on what we've done:

  • Equation: x - 68 = 31
  • To solve the equation, add 68 to both sides of the equation.
  • To check the solution, substitute 99 for the variable in the equation.

Therefore, the complete response would be:

  • Equation: \( x - 68 = 31 \)
  • To solve the equation, add 68 to both sides of the equation.
  • To check the solution, substitute 99 for the variable in the equation.