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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. Techniques for eliminating decimals and fractions, as well as solving for the variable in different types of linear equations. Additionally, it includes word problems related to real-world scenarios, such as tracking the levels of mercury in bodies of water and saving money for a marathon. The document aims to equip students with the necessary skills and strategies to confidently solve linear equations with variables on both sides, which is a fundamental concept in algebra and mathematics.
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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
Which number can each term of the equation be multiplied by to eliminate the decimals before solving? 5.6j - 0.12 = 4 + 1.1j - Answer: 100 What is the solution to the linear equation? 4b + 6 = 2 - b + 4 - Answer: b = 0 The levels of mercury in two different bodies of water are rising. In one body of water the initial measure of mercury is 0.05 parts per billion (ppb) and is rising at a rate of 0.1 ppb each year. In the second body of 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.
6 - 3/4x + 1/3 = 1/2x + 5 - Answer: 12 What is the solution to the linear equations? 2/3x - 1/2 = 1/3 + 5/6x - Answer: x = - 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 What is the solution to the linear equation? d - 10 - 2d + 7 = 8 + d - 10 - 3d - Answer: d = 1 Solve the equation. -3x + 1 + 10x = x + 4 - Answer: x = 1/ 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
