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A comprehensive overview of solving linear equations using the distributive property. It includes a series of practice problems with step-by-step solutions, covering a wide range of scenarios such as equations with fractions, equations with multiple terms, and equations with no solutions. Designed to help students develop a strong understanding of the distributive property and its application in solving linear equations. It covers topics such as identifying the number of solutions, solving for specific variables, and interpreting partial solutions. Likely intended for use in a mathematics course, potentially at the high school or early college level, and could be valuable for students preparing for exams or seeking to improve their problem-solving skills in this area.
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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 Solve for x. 9(x + 1) = 25 + x - Answer: x = 2 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
What is the value of x in the equatjon 2.5(6x - 4) = 10 + 4(1.5 + 0.5x)? - Answer: 2 Lily begins solving the equation 4(x - 1) - x = 3(x + 5) - 11. Her work is shown below. How can her partial solution be interpreted? - Answer: The equation has no solution. What us the value of n in the equation 1/2(n - 4) - 3 = 3 - (2n + 3)? n = - Answer: 2 How many solutions exist for the given equation solution? 3x + 13 = 3(x + 6) + 1 - Answer: zero
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
