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A comprehensive overview of solving linear equations using the distributive property. It covers a variety of practice problems with certified answers, ranging from equations with no solutions to those with infinitely many solutions. Structured in a question-and-answer format, allowing students to test their understanding of the concepts and techniques involved in solving linear equations. The content is suitable for students at the high school or university level who are studying algebra and linear equations. The document could be used as study notes, lecture notes, or a summary to prepare for exams, assignments, or university essays related to the topic.
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Which equation has no solution? - Answer: 5 + 2(3 + 2x) = x + 3(x + 1) Solve for n. n + 1 = 4(n - 8) - Answer: n = 11 How many solutions exist for the given equation?
0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20) - Answer: one How many solutions exist for the given equation? 3(x - 2) = 22 - x - Answer: one Solve for x. 6(x - 1) = 9(x + 2) - Answer: x = - Solve for x. 9(x + 1) = 25 + x - Answer: x = 2 Kate begins solving the equation 2/3(6x - 3) = 1/2(6x - 4). Her work is correct and is shown below. When she adds 2 to both sides, the equation 4x = 3x results. Which is the best interpretation of this equation? - Answer: The equation has one solution: x = 0.
What us the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)? - Answer: 4 Solve for x. 5(x - 10) = 30 - 15x - Answer: x = 4 How many solutions exist for the given equation? 1/2(x + 12) = 4x - 1 - Answer: one Karissa begins to solve the equation 1/2x (x - 14) + 11 = 1/2x - (x - 4). Her work is correct and is shown below. When she subtracts 4 from both sides, 1/2x = -1/2x results. What is the value of x? - Answer: 0 What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x -2)? - Answer: 4
How many solutions exist for the given equations? 12x + 1 = 3(4x + 1) -2 - Answer: infinitely many
