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Chapter 0: Problem 16

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

Short Answer

Expert verified
The solution to the equation is \(x = \frac{25}{7}\).

Step by step solution

01

Clearing the Fractions

This equation has denominators of 5, 2, and 3. In this step, we will multiply the entire equation by 30 (the least common multiple of 5, 2, and 3) to get rid of the fractions. After doing so, the equation becomes \(18x - 15(x - 3) = 10(x + 2)\).
02

Distributing and Simplifying

Distribute the numbers being multiplied by the parentheses. Multiplying -15 into the (x - 3) gives us -15x + 45. Also, multiplying 10 into the (x + 2) gives us 10x + 20. Therefore, the equation becomes \(18x - 15x + 45 = 10x + 20\). Adding like terms on each side of the equation yields \(3x + 45 = 10x + 20\).
03

Solving for x

First, subtract 3x from each side of the equation to get \(45 = 7x + 20\). Then, subtract 20 from each side of the equation to isolate the x term yielding \(25 = 7x\). Finally, divide each side by 7 to solve for x which gives \(x = \frac{25}{7}\).

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$x^{2}+36=(x+6)^{2}$$

Describe how to solve an absolute value inequality involving the symbol <. Give an example.

Explain how to add rational expressions having no common factors in their denominators. Use \(\frac{3}{x+5}+\frac{7}{x+2}\) in your explanation.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{x^{2}-25}{x-5}=x-5$$

Perform the indicated operations. Simplify the result, if possible. $$\frac{y^{-1}-(y+2)^{-1}}{2}$$
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