1. **Solve the equations algebraically.** a. $\frac{x-2}{3} + \frac{x+5}{3} = \frac{1}{6}$ Work shown: - Multiply both sides by 6 to eliminate the fraction: $2x - 4 + 3x + 15 = 1$ - Combine like terms: $5x + 11$ - Correct equation: $5x - 11 = 2$ b. $6x^2 + 7x = 3$ c. $|4x + 1| = 3$ d. $4x^2 - 4x + 2 = 0$

1. Solve the equations algebraically. a. $\frac{x-2}{3} + \frac{x+5}{3} = \frac{1}{6}$ Work shown: - Multiply both sides by 6 to eliminate the fraction: $2x - 4 + 3x + 15 = 1$ - Combine like terms: $5x + 11$ - Correct equation: $5x - 11 = 2$ b. $6x^2 + 7x = 3$ c. $|4x + 1| = 3$ d. $4x^2 - 4x + 2 = 0$

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

1. **Solve the equations algebraically.**

a. $\frac{x-2}{3} + \frac{x+5}{3} = \frac{1}{6}$

Work shown:
- Multiply both sides by 6 to eliminate the fraction: $2x - 4 + 3x + 15 = 1$
- Combine like terms: $5x + 11$
- Correct equation: $5x - 11 = 2$

b. $6x^2 + 7x = 3$

c. $|4x + 1| = 3$

d. $4x^2 - 4x + 2 = 0$

Expert Solution

Step 1

given the equations we need to solve them algebraiacally.

$\frac{x - 2}{3} + \frac{x + 5}{2} = \frac{1}{3} t a k i n g L C M o n L H S \frac{2 (x - 2) + 3 (x + 5)}{6} = \frac{1}{3} \frac{2 x - 4 + 3 x + 15}{6} = \frac{1}{3} 5 x + 11 = \frac{6}{3} 5 x + 11 = 2 5 x = 2 - 11 5 x = - 9 x = \frac{- 9}{5}$