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ExamplesExample 6 Solve:
Solution We can multiply both sides by any nonzero number we like. Since
1x = 8 Simplifying x = 8 Using the identity property of 1 Check: The solution is 8. In Example 6, to get x alone, we multiplied by the reciprocal, or
multiplicative inverse of Because division is the same as multiplying by a reciprocal, the multiplication principle also tells us that we can divide both sides by the same nonzero number. That is, if a = b then In a product like 3x , the multiplier 3 is called the coefficient. When the coefficient of the variable is an integer or a decimal, it is usually easiest to solve an equation by dividing on both sides. When the coefficient is in fraction notation, it is usually easier to multiply by the reciprocal. Example 7 Solve: Solution a) 1x = -23 Simplifying x = -23 Using the identity property of 1 Check: The solution is -23. b)
Check: The solution is 4.2. c) To solve an equation like -x = 9 remember that when an expression is multiplied or divided by -1 its sign is changed. Here we multiply both sides by -1 to change the sign of -x : -x = 9 (-1)(-x) = (-1)9 Multiplying both sides by -1 (Dividing by -1 would also work) x = -9 Note that (-1)(-x) is the same as (-1)(-1)x Check: The solution is -9. d) To solve an equation like
y = 12 Check: The solution is 12. |