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Equations

When solving equations, the goal is to find the unknown value that can replace the variable (often x) so that there is "balance" between the left and right sides of the equation.

You can think of equations like a scale – both sides of the equals sign must be in "balance."

5 = 5

Here, the scale is balanced

4 = 5

Here, the scale is unbalanced, something is wrong

x + 4 = 5

The scale is balanced when x = 1

Rules for Solving Equations:

  • You may add the same number to both sides of the equation.
  • You may subtract the same number from both sides of the equation.
  • You may multiply both sides of the equation by the same number (as long as the number is not 0).
  • You may divide both sides of the equation by the same number (as long as the number is not 0).
  • You may raise both sides of the equation to the same power.
  • You may take the same root of both sides of the equation.

REMEMBER:
If you multiply or divide, you must apply the operation to all terms on both sides of the equation!
If you're unsure, you can place the entire expression inside parentheses before adding, subtracting, multiplying, or dividing to ensure the operation is applied correctly.

Note:

Often, the letter x is used to represent an unknown value.
When solving equations, the goal is to isolate x on one side of the equation so that you can determine the unknown value "x."
A good starting point is to collect all the x terms on the side where there