Solve each problem. Which one or more of the following cannot ...

Question

Solve each problem. Which one or more of the following cannot be a correct equation to solve a geometry problem, if x represents the length of a rectangle? (Hint: Solve each equation and consider the solution.) A. 2x+2(x- 1) = 14 B. -2x+7(5-x) = 52 C. 5(x+2)+5x = 10 D. 2x+2(x-3) = 22

Accepted Answer

Welcome back. I am so glad you're here. We are given this practice problem. We are asked to determine which of the following equations will not give a valid value of the side length of a square. Supposing that the square side length is represented by X. Well, what are all of the possible values for the side length of a square? Well, I mean, really the side length of a square could be anything as long as it is greater than zero. So we've got these four equations here. We just have to figure out which one does not fit our given domain of X is greater than zero. So let's work on solving answer A we've got three X plus two times parentheses, X plus 10, end parentheses equals 40. The first step here will be to do the distribution, distributing to two X and 10 in parentheses. So we can bring down three X and then we've got plus two times X is two X plus two times 10 is 20 still equals 40. Now, we can combine like terms on the left. We have three X plus two X and those together equal five X bring down that plus 20 still equals 40. Now, we want to bring the constant terms together on the side opposite of the X. So we can subtract 20 from both sides of the equation. We'll have five x, those twenties cancel out on the left equals 40 -20 is 20. Now to get X totally by itself, we want to divide both sides by five. And on the left five divided by five is once we have one X, which is just X and we get X equals 20 divided by five, which is four that fits our domain X is greater than zero. So this one is plausible. Now, let's try and work another one. We've got negative four, X plus five parentheses, four minus two X, end parentheses equals 28. So for answer choice, B again, let's start off with the distribution, distributing the five to the four and the negative two X. So we can bring down this negative four, X five times four is 20. So plus 20 and five times negative two, X is minus 10, X still equals 28. Now, we can combine like terms, we have negative four, X minus 10, X and negative four, X minus 10, X equals negative 14 X still plus 20 equals 28. And now again, we want those constant terms together on the opposite side of the equation as the X. So we can subtract 20 from both sides. And we still have negative 14 X on the left and that equals A, an 8 28 minus 20 equals eight. And now to get that X by itself, we want to divide both sides by the negative 14. On the left negative 14, divided by negative 14 is one or just X and on the right eight divided by negative 14. Well, that's a fraction. We could simplify it, but it's a negative fraction. And noting that that is negative, that is outside of our possible domain. So answer choice B does not give a valid length of the side of a square. So answer Choice B works well done. We'll catch you on the next one.

Solve each problem. Which one or more of the following cannot be a correct equation to solve a geometry problem, if x represents the length of a rectangle? (Hint: Solve each equation and consider the solution.) A. 2x+2(x- 1) = 14 B. -2x+7(5-x) = 52 C. 5(x+2)+5x = 10 D. 2x+2(x-3) = 22

Key Concepts

Formulating and Solving Linear Equations

Interpreting Solutions in Context

Distributive Property and Simplification

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