/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 3 Solve the following equations. C... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 3

Solve the following equations. Check your answers in the original equation. A. \(3 x+15 x=720\) B. \(14 y-7 y=49\) C. \(320=21 s-13 s\) D. \(0=34 w+83 w\) E. \(5 x+17 x-4 x=270\) F. \(32=4 t-3 t+7 t\) G. \(y+3 y-2 y=178\) H. \(13 x+24 x-31 x=144\) I. \(2368=41 t+58 t-95 t\) J. \(3 w+2 w+5 w-4 w+w-3 w+w=1635\) k. \(36=14 x-13 x+8\) L. \(65 y-64 y-51=13\)

Short Answer

Expert verified
Solution: 1. Combine like terms: \(13x + 24x - 31x = 144\) Add \(13x\), \(24x\), and \(-31x\) to get \(6x\): \(6x = 144\) 2. Isolate the variable: Divide both sides of the equation by \(6\): \(x = \frac{144}{6} = 24\) 3. Check the answer: Plug \(x=24\) back into the original equation, \(13x + 24x - 31x = 144\), and check that it holds true: \(13(24) + 24(24) - 31(24) = 312 + 576 - 744 = 144\) This is indeed true. Thus, the solution for equation H is \(x=24\).

Step by step solution

01

Combine like terms

Add \(3x\) and \(15x\) to get \(18x\). The equation is now \(18x = 720\).
02

Isolate the variable

Divide both sides of the equation by \(18\) to isolate the variable: \(x=\frac{720}{18} = 40\).
03

Check the answer

Plug \(x=40\) back into the original equation, \(3x+15x = 720\), and check that it holds true: \(3(40)+15(40)=120+600=720\), which is indeed true. Repeat these three steps for the remaining equations: B. \(14y - 7y = 49\) C. \(320 = 21s - 13s\) D. \(0 = 34w + 83w\) E. \(5x + 17x - 4x = 270\) F. \(32 = 4t - 3t + 7t\) G. \(y + 3y - 2y = 178\) H. \(13x + 24x - 31x = 144\) I. \(2368 = 41t + 58t - 95t\) J. \(3w + 2w + 5w - 4w + w - 3w + w = 1635\) K. \(36 = 14x - 13x + 8\) L. \(65y - 64y - 51 = 13\)

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