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Which of the following statements are true of solving equations?You are using inverse operations to isolate the variable.The addition property is usually used first.You are making a good guess at the solution.Order of operations is often done in reverse order.There are usually two solutions for a linear equation.

Question

Which of the following statements are true of solving equations?You are using inverse operations to isolate the variable.The addition property is usually used first.You are making a good guess at the solution.Order of operations is often done in reverse order.There are usually two solutions for a linear equation.

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Solution

To determine which of the statements are true of solving equations, let's analyze each statement one by one:

  1. "You are using inverse operations to isolate the variable." This statement is true. When solving an equation, we use inverse operations to isolate the variable on one side of the equation.

  2. "The addition property is usually used first." This statement is not necessarily true. The addition property can be used at any step of solving an equation, depending on the specific equation and the desired approach.

  3. "You are making a good guess at the solution." This statement is not true. Solving equations involves applying mathematical operations and principles to find the exact solution, rather than relying on guesswork.

  4. "Order of operations is often done in reverse order." This statement is true. When solving equations, we often work in reverse order of the usual order of operations. This is done to isolate the variable and simplify the equation step by step.

  5. "There are usually two solutions for a linear equation." This statement is not necessarily true. A linear equation can have one solution, infinitely many solutions, or no solution, depending on the specific equation and its coefficients.

In summary, the true statements about solving equations are:

  • You are using inverse operations to isolate the variable.
  • Order of operations is often done in reverse order.

The false statements are:

  • The addition property is usually used first.
  • You are making a good guess at the solution.
  • There are usually two solutions for a linear equation.

This problem has been solved

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