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MAT111 ALGEBRA REVIEW Three Basic Rules epw 11/1/06 1 MAT111 Three Basic Rules • Add or subtract the same quantity on both sides of the equation • Multiply or divide both sides of the equation by the same quantity (as long as that quantity is not zero) • Interchange the left and right sides of an equation epw 11/1/06 2 MAT111 Three Basic Rules (cont.) What good are the three basic rules? To help solve equations that involve unknowns! epw 11/1/06 3 MAT111 Adding and Subtracting Examples Problem: Solve the equation x 8 = 4 for x Solution: Isolate x by adding 8 to both sides x 8 8 = 4 8 x = 12 Problem: Solve the equation y 5 = 2y for y Solution: Isolate y by subtracting y from both sides y 5 y = 2y y 5 = y (interchanging both sides) y = 5 epw 11/1/06 4 MAT111 More Examples • What if there is more than one unknown? Problem: Solve 7q – 16 = p + 4q – 2 for p Solution: Isolate p by subtracting 4q from both sides and adding 2 to both sides 7q – 16 – 4q + 2 = p + 4q – 4q – 2 + 2 3q – 14 = p (interchanging both sides) p = 3q – 14 Note: We cannot state a numerical value for p until we know the value of q epw 11/1/06 5 MAT111 Multiplying and Dividing Examples Problem: Solve the equation 5x = 25 for x Solution: Isolate x by dividing both sides by 5 5 x 25 x5 5 5 3 z Problem: Solve the equation 2 10 for z 4 Solution: Isolate z by adding 2 to both sides, then multiply both sides by 4/3 3z 3z 3z 4 4 2 2 10 2 12 12 z 16 4 4 4 3 3 epw 11/1/06 6