Combine like terms such that each variable only appears once. 3 4 x + 1 2 x \frac34x+\frac12x

Here we're asked to combine like terms such that each variable appears only once. Looking at our expression here, we have three fourths x plus one half x. Now, looking at these two terms, they both have a variable x with no exponent, which remember, implies having an exponent of one. So these are terms with the same variable raised to the same exponent, meaning they are like terms. So we can combine them by adding their coefficients. Now here, our coefficients are fractions, three fourths and one half. And they don't currently have the same denominator. So we need to make them have the same denominator so that we can add them together. Now looking at these two fractions, three fourths and one half, I can easily make one half have that same denominator of four by simply multiplying by two over two. So multiplying here, that gives me two over four. Now thinking about this logically, thinking about the fraction one half, if I were to ask you what is half of four, you would tell me two. So it makes sense that the fraction that we get here is then two fourths. So now that I've written this to have a like denominator or common denominator, this is three fourths x plus two fourths x, having written that equivalent fraction. So now I can add these like terms together by adding those coefficients three fourths plus two fourths. When adding fractions with like denominators, we can just add those numerators together. So three plus two gives me five, so this is five fourths x. So now we've combined our like terms such that our variable x appears only once. Let us know if you have questions and I'll see you in the next one.

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Multiple Choice

Combine like terms such that each variable only appears once.
$\frac{3}{4} x + \frac{1}{2} x$

$\frac{4}{6} x$

$\frac{3}{8} x$

$\frac{5}{4} x$

$\frac{1}{4} x$

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Verified step by step guidance

Identify the like terms in the expression. Here, all terms have the variable $x$, so they can be combined by adding their coefficients.

Write down the coefficients of each term as fractions: $\frac{3}{4}$, $\frac{1}{2}$, $\frac{4}{6}$, and $\frac{3}{8}$.

Find a common denominator for all the fractions to add them easily. The denominators are 4, 2, 6, and 8. Determine the least common denominator (LCD).

Convert each fraction to an equivalent fraction with the LCD as the denominator, then add all the numerators together while keeping the denominator the same.

Write the sum of the coefficients as a single fraction multiplied by $x$, which gives the combined like terms with $x$ appearing only once.

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Combine like terms such that each variable only appears once.34x+12x\frac34x+\frac12x

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Combine like terms such that each variable only appears once.
$\frac{3}{4} x + \frac{1}{2} x$