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Chapter 0: Problem 11

Solve each linear equation. $$\frac{x+3}{6}=\frac{3}{8}+\frac{x-5}{4}$$

Short Answer

Expert verified
The solution to the equation is \(x = 16.5\).

Step by step solution

01

Combining Like Terms

First, combine like terms on each side of the equation. This means to combine terms that have the same variable. For this equation, it's just a matter of properly ordering the equation. So the original equation \(\frac{x+3}{6}=\frac{3}{8}+\frac{x-5}{4}\) becomes \(\frac{x+3}{6}-\frac{x-5}{4}=\frac{3}{8}\)
02

Clear Denominators

Next, clear denominators to remove the fractions from the equation. This can be done by finding a common denominator for all fractions in the equation and multiply on each side. In this case, the common denominator is 24. This results in the equation \(4(x+3)-6(x-5)=3*3\)
03

Simplify the Equation

After we have cleared the denominators, the next step is to simplify the expression. This is done by expanding the brackets and simplifying the resulting expression. Expanding the brackets results into \(4x+12-6x+30=9\) and simplifying this expressions gives \(-2x + 42 = 9\)
04

Solve for x

Finally, solve for the variable x. This is done by subtracting 42 from both sides of the equation to isolate the term with x, which gives \(-2x = 9 - 42\). Then divide by -2 on both sides to solve for x, which gives \(x = (9 - 42) / -2\)

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