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A comprehensive guide to solving linear equations with variables on both sides. It covers various examples and step-by-step solutions, including questions and correct answers. Designed to help students understand the concepts and techniques involved in solving these types of equations. It covers topics such as the subtraction property of equality, eliminating fractions, and solving for variables. Likely intended for use as study notes, lecture notes, or a summary for students preparing for exams or assignments related to linear equations. The content is structured in a clear and organized manner, making it a valuable resource for university-level mathematics courses, particularly those focused on algebra and problem-solving.
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Two runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and will save $ each month. The second runner has $50 in savings and will save $ each month.
Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money? - Answer: 112 + 25m + 45 = 50 + 60m Solve the equation. y + 3 = -y + 9 - Answer: y = 3 What is the justification for the step taken from line 2 to line 3? 3x + 9 - 7x = x + 10 + x - Answer: the subtraction property of equality Solve the equation. 8 - 2x = -8x + 14 - Answer: x = 1 Which number can each term of the equation be multiplied by to eliminate the fractions the fractions before solving? -3/4m -1/2 = 2 + 1/4m - Answer: 4
water the initial measure is 0.12 ppb and the rate of increase is 0. ppb each year. Which equation can be used to find y, the year in which both bodies of water have the same amount of mercury? - Answer: 0.05 + 0.1y = 0.
The International Business Club starts the school year with $250.50 in their account. They spend $35 each month on activities. The Future Agricultural Leaders Club starts with $300 and spends $45.25 each month. Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money? - Answer: 250.5 - 35m = 300 - 45.25m What is the solution to the linear equation? 2/5 + p = 4/5 + 3/5p - Answer: p = 1 Which number can each term of the equation be multiplied by to eliminate the decimals before solving? -m + 0.02 + 2.1m = -1.45 _ 4.81m - Answer: 100
