Overview:
Although some simple equations or inequalities call for one type of operation, many call for two or three steps. In that case, read the problem carefully to determine what operations are needed. Then solve the problem by working backwards.
Be Sure What the Problem Is Asking
Read the problem to determine what operations are needed and if the problem is asking for more than one operation. Is the problem asking for addition, subtraction, multiplication, or division? In order to undo addition, use the inverse, subtraction. In order to undo multiplication, use the inverse, division.
Work Backwards to Solve the Equation
For example, suppose the problem is 42 = 10 +2p. Use the inverse, subtraction, to solve the addition, by subtracting 10 from both sides, as in 42 – 10 = 10 – 10 + 2p or 32 = 2p. Then use the inverse, division, to solve the remaining multiplication problem, as in 32/2 = 2p/2, 16 = p. If the problem is x/4 +9 = 6, use the inverse, subtraction, to solve the addition first, as in x/4 + 9 – 9 = 6 – 9 to give x/4 = -3. Then use the inverse, multiplication, to solve the division as 4(x/4) = 4 (-3), or x = -12.
Be Sure What the Inequality Is Asking
Inequalities are similar to equations in that the problem will require careful reading to determine what operations are needed and if the problem is asking for more than one operation. For example, suppose the problem is 3x – 1 >14. In order to solve the problem, two operations are needed. Addition is the inverse of subtraction, and division is the inverse of multiplication.
Work Backwards to Solve the Inequality
Similar to the process for solving equations, work backwards to solve the inequality. Using the example 3x – 1 >14, 3x – 1 + 1 > 14 + 1, because addition is the inverse of subtraction. Then 3x >15, so 3x/3 >15/3, because division is the inverse of multiplication, so x>5.
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