A.)List the 4 steps outlined in the lesson on solving equations.
1 answer:
1.) Solve for x: 5 x + 7 = 3 x + 21 Subtract 3 x from both sides: (5 x - 3 x) + 7 = (3 x - 3 x) + 21 5 x - 3 x = 2 x: 2 x + 7 = (3 x - 3 x) + 21 3 x - 3 x = 0: 2 x + 7 = 21 Subtract 7 from both sides: 2 x + (7 - 7) = 21 - 7 7 - 7 = 0: 2 x = 21 - 7 21 - 7 = 14: 2 x = 14 Divide both sides of 2 x = 14 by 2: (2 x)/2 = 14/2 2/2 = 1: x = 14/2 The gcd of 14 and 2 is 2, so 14/2 = (2×7)/(2×1) = 2/2×7 = 7:Answer: x = 7 ____________________________________________________________ 2.) Solve for x: 3 x - 2 (5 - x) = 3 x - 3 (x - 10) -2 (5 - x) = 2 x - 10: 2 x - 10 + 3 x = 3 x - 3 (x - 10) Grouping like terms, 3 x + 2 x - 10 = (3 x + 2 x) - 10: (3 x + 2 x) - 10 = 3 x - 3 (x - 10) 3 x + 2 x = 5 x: 5 x - 10 = 3 x - 3 (x - 10) -3 (x - 10) = 30 - 3 x: 5 x - 10 = 30 - 3 x + 3 x 3 x - 3 x = 0: 5 x - 10 = 30 Add 10 to both sides: 5 x + (10 - 10) = 10 + 30 10 - 10 = 0: 5 x = 30 + 10 30 + 10 = 40: 5 x = 40 Divide both sides of 5 x = 40 by 5: (5 x)/5 = 40/5 5/5 = 1: x = 40/5 The gcd of 40 and 5 is 5, so 40/5 = (5×8)/(5×1) = 5/5×8 = 8: <span>Answer: x = 8 _________________________________________________________ 3.) Solve for x:</span> 5 (x + 1) = 3 (2 x + 3) + 5 3 (2 x + 3) = 6 x + 9: 5 (x + 1) = 6 x + 9 + 5 Grouping like terms, 6 x + 5 + 9 = 6 x + (9 + 5): 5 (x + 1) = 6 x + (9 + 5) 9 + 5 = 14: 5 (x + 1) = 6 x + 14 Expand out terms of the left hand side: 5 x + 5 = 6 x + 14 Subtract 6 x from both sides: (5 x - 6 x) + 5 = (6 x - 6 x) + 14 5 x - 6 x = -x: -x + 5 = (6 x - 6 x) + 14 6 x - 6 x = 0: 5 - x = 14 Subtract 5 from both sides: (5 - 5) - x = 14 - 5 5 - 5 = 0: -x = 14 - 5 14 - 5 = 9: -x = 9 Multiply both sides of -x = 9 by -1: (-x)/(-1) = -9 (-1)/(-1) = 1: <span>Answer: x = -9 </span>
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