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Chapter 7: Problem 103

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{x^{2}+3}{3}=x^{2}+1$$

Short Answer

Expert verified
The statement \(\frac{x^{2}+3}{3}=x^{2}+1\) is False. The correct statement to make it True is \(\frac{x^{2}}{3}+1 = x^{2}+1\).

Step by step solution

01

Simplify the left side of the equation

Start by simplifying the left side of the equation, which involves a division. Divide each term in the numerator by 3. So, the simplified version of \(\frac{x^{2}+3}{3}\) becomes \(\frac{x^{2}}{3}+1\).
02

Compare the left side with the right side

After simplifying the left side, it's time to compare it with the right side of the equation. If \(\frac{x^{2}}{3}+1 = x^{2}+1\), the original statement is true; otherwise, it's false.
03

Correcting the false statement

After comparison, it's found that the original statement is false as \(\frac{x^{2}}{3}+1\) is not equal to \(x^{2}+1\). In order to make the statement true, the correct statement should be \(\frac{x^{2}}{3}+1 = x^{2}+1\).

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Most popular questions from this chapter

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x}{x-y}+\frac{y}{y-x}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{y-3}{y^{2}-25}+\frac{y-3}{25-y^{2}}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can solve \(\frac{x}{9}=\frac{4}{6}\) by using the cross-products principle or by multiplying both sides by \(18,\) the least common denominator.

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Add or subtract as indicated. Simplify the result, if possible. $$\frac{x}{x+7}-1$$
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