/*! 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 13 Solve each linear equation. $$... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 13

Solve each linear equation. $$\frac{x}{4}=2+\frac{x-3}{3}$$

Short Answer

Expert verified
The solution to the equation is \(x = -12\).

Step by step solution

01

Clear the fractions

To make the equation easier to solve, clear fractions by multiplying each term by the denominator of the fractions, which is 12 in this case. This gives:\n \(3x = 24 + 4(x - 3)\)
02

Simplify the equation

Simplify the right side of the equation by multiplying 4 through the parentheses. This gives:\n \(3x = 24 + 4x - 12\)
03

Further simplification

Continue to simplify the equation by adding up like terms on the right side, resulting in:\n \(3x = 4x + 12\)
04

Isolate x on one side

To isolate \(x\) on one side of the equation, subtract \(3x\) from both sides, giving:\n \(0 = x + 12\)
05

Solve for x

Finally solve for \(x\) by subtracting 12 from both sides of the equation. The solution is:\n \(x = -12\)

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Most popular questions from this chapter

a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$ \text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. } $$ How old is the son?b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}+2^{-1}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?

What is a linear equation in one variable? Give an example of this type of equation.

In solving \(\sqrt{2 x-1}+2=x,\) why is it a good idea to isolate the radical term? What if we don't do this and simply square each side? Describe what happens.

Perform the indicated operations. $$\frac{1}{x^{n}-1}-\frac{1}{x^{n}+1}-\frac{1}{x^{2 n}-1}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$x^{3}-64=(x+4)\left(x^{2}+4 x-16\right)$$
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