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How Do You Solve a Two-Step Equation by Multiplying by -1?

Solve the equation -b + 4 = - 3 for b.

Summary

  1. 'b' is the variable we're solving for
  2. To isolate 'b', we need to get it by itself on one side of the equals sign
  3. We need to subtract 4 from both sides to keep the equation equal
  4. Multiplying by -1 will change the sign of 'b' from negative to positive
  5. We need to multiply by -1 on both sides to keep the equation equal
  6. To check the answer, plug 7 in for 'b' in the original equation
  7. The '?' means that we're not sure if the two sides are equal

Notes

    1. 'b' is the variable we're solving for
    2. To isolate 'b', we need to get it by itself on one side of the equals sign
    3. To do this, we'll need to to subtract 4 from both sides of the equation
    1. Subtracting 4 will get the 'b' term by itself on the left side
    2. The Subtraction Property of Equality says that we need to subtract 4 from both sides to keep the equation equal
    1. Remember, 'b' is the variable we're solving for, not '-b'
    2. So we need to find a way to get rid of that negative sign
    1. Multiplying something by -1 will flip its sign
    2. So we can multiply '-b' by -1 to change it to a positive 'b'
    3. But if we do that, we need to multiply the other side of the equation by -1 too
    4. That way the two sides of the equation will still be equal
    1. Don't forget, we need to multiply both sides of an equation by the same number to keep the equation equal
    2. So we also need to multiply the right hand side by -1
    1. Just like multiplying '-b' by -1 makes it positive 'b', multiplying -7 by -1 makes it positive 7
    1. To check the answer, we have to plug the answer we got into the original equation
    2. If we get a true statement, we know the answer is correct
    1. If we get a true statement, we know the answer is correct
    2. If the equation then turns into a true statement, we know the answer is correct