Overview:
Some simple equations, such as a + 4 = 12 and 2x = 16, only take one step to solve. This is because it only takes one operation to solve the equation, with no other operations to be performed. Other equations require more than one mathematical operation for the variable to be solved.
What Operations Are Needed to Solve the Problem?
Read the problem carefully to determine what operations are needed to solve the problem. In order to solve an equation such as a + 4 = 12, the operation that is needed is subtraction. Once 4 is subtracted from both sides of the equation, nothing more needs to be done to find the solution. Similarly, with an equation such as 2x = 16, once both sides of the equation are divided by 2, nothing more needs to be done. However, if the problem is 5x + 2 = 27, two different operations need to be done to solve the equation, both subtraction and division.
Is the Equation Solved After One Step?
After determining what operations are needed to solve the problem, the next step is to solve the problem. For example, if 1/3 y = 4, 3 ∙1/3 y = 4∙3, or y = 12. Both sides of the equations are multiplied by 3 to solve the problem. If a + 4 – 4 = 12 – 4, then a equals 8. The number 4 is subtracted from both sides of the equation. In both of those equations, the equation is solved in just one step.
What About the Next Step?
If the first operation doesn’t solve the problem, go on to the next operation. For example, if the problem is 5x + 2 = 27, start by subtracting 2 from each side of the equation. In the first step, 5x + 2 -2 = 27 – 2 or 5x = 25. The equation still isn’t quite solved. In the next step 5x/5 = 25/5, or x = 5, which solves the equation. Similarly, suppose the problem is y2 + 9 = 25. In that case, y2 + 9 – 9 = 25 – 9, or y2= 16. Going on to the next operation, y = 4, and the equation is fully solved.
What About Checking Work?
The process of checking work is similar, no matter how many steps there are to the equation. If the solution a = 8 is correct for a +4 = 12, then 8 + 4 = 12. If x = 5 is correct for the sentence 5x +2 = 27, then replacing 5(5) + 2 = 27 is also correct.
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