MAT111 epw 11/1/061 ALGEBRA REVIEW Three Basic Rules

MAT111 epw 11/1/062 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

MAT111 epw 11/1/063 Three Basic Rules (cont.) What good are the three basic rules? To help solve equations that involve unknowns!

MAT111 epw 11/1/064 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 = 2 y for y Solution: Isolate y by subtracting y from both sides y  5  y = 2 y  y  5 = y (interchanging both sides)  y = 5

MAT111 epw 11/1/065 More Examples What if there is more than one unknown? Problem: Solve 7 q – 16 = p + 4 q – 2 for p Solution: Isolate p by subtracting 4 q from both sides and adding 2 to both sides 7 q – 16 – 4 q + 2 = p + 4 q – 4 q –  3 q – 14 = p  (interchanging both sides)  p = 3 q – 14 Note: We cannot state a numerical value for p until we know the value of q

MAT111 epw 11/1/066 Multiplying and Dividing Examples Problem: Solve the equation 5 x = 25 for x Solution: Isolate x by dividing both sides by 5 Problem: Solve the equation for z Solution: Isolate z by adding 2 to both sides, then multiply both sides by 4/3