Because an equation represents a scale, it can also be manipulated like one. The diagram below shows a simple equation and the steps to solving it.
Initial Equation / Problem \( x + 23 = 45 \)
Subtract 23 from each side \( x + 23 – 23= 45 – 23 \)
Result / Answer x = 22
The diagram below shows a more complex equation. This equation has both a constant and a variable on each side. Again, to solve this you must keep both sides of the equation equal; perform the same operation on each side to get the variable “x” alone. The steps to solving the equation are shown below.
Initial Equation / Problem: \( x + 23 = 2x + 45 \)
Subtract x from each side \( x – x + 23 = 2x – x + 45 \)
Result 23 = x + 45
Subtract 45 from each side [math] 23 – 45 = x + 45 – 45 [/math]
Result -22 = x
Answer x = -22