# By William Huang. Solve Problems by writing and solving equations (Math Textbook)

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By William Huang

Solve Problems by writing and solving equations (Math Textbook)

Phase 1: UNDERSTAND the problem What am I trying to find? What data am I given? Have I ever solved a similar problem? Phase 2: Develop and carry out a PLAN What strategies might I use to solve the problem? How can I correctly carry out the strategies I selected? Phase 3: Find the ANSWER and CHECK Does the proposed solution check? What Is the answer to the problem? Does the answer seem reasonable? Have I stated the answer clearly? (Math Textbook)

Ex. Translate to an equation and solve If you subtract a number from four times its square, the result is three (math textbook).

(If you subtract a number from four times its square, the result is three) Number = n Four times its (the n’s) square = 4n 2 The result is three = 3 If you subtract a number from four times its square, the result is three. If you subtract n from 4n 2, the result is 3 4n 2 – n = 3 What the question really means: Solve for n 4n 2 – n = 3 4n 2 – n -3 = 3 -3 Subtract 3 from both sides 4n 2 – n – 3 = 0 -12 -4 3 -4n 3n 4n 2 -3 34n n =(4n+3)(n-1) = 0 Factor

(4n+3)(n-1) = 0 4n + 3 = 0 4n = -3 n = 3 – 4 n – 1 = 0 n = 1 Subtract 3 from both sides Divide both sides by 3 Add 1 to both sides - n = 1 or 3 – 4 -

The product of two consecutive integers is 182, what are the integers? (math textbook) n = 1 st integer n + 1 = 2 nd consecutive integer because consecutive means “next” n (n + 1) = 182 n 2 + n = 182 n 2 + n -182 = 0 -182 1 14-13 These are your answers Answer: 13 and 14 or -13 and -14 Simplify Subtract 182 from both sides Factor The answer can be positive or negative as long as both of them are positive or negative because 13 x 14 =182 and -13 x -14 =182.

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