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Chapter 0: Problem 15

Solve each linear equation. $$\frac{x+1}{3}=5-\frac{x+2}{7}$$

Short Answer

Expert verified
The solution to the equation \(\frac{x+1}{3} = 5 - \frac{x+2}{7}\) is \(x = 9.2\).

Step by step solution

01

Remove the Fraction

To get rid of the fractions, multiply every term by the least common multiple (LCM) of the denominators which in this case is 21.
02

Simplify the equation

After multiplying each term by 21, the equation becomes: \(7(x+1) = 105- 3(x+2)\). Expand to simplify; it becomes \(7x+7 = 105 - 3x - 6\).
03

Group like terms

Combine like terms and group them on one side of the equation to isolate the variable x. This gives: \(7x+3x = 105 -6 -7\). Which simplifies to: \(10x = 92\).
04

Solve for x

To solve for x, divide both sides of the equation by 10. This gives: \(x = \frac{92}{10}\), thus \(x = 9.2\).

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Most popular questions from this chapter

Describe two ways to simplify \(\frac{\frac{3}{x}+\frac{2}{x^{2}}}{\frac{1}{x^{2}}+\frac{2}{x}}\).

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