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Rewrite the equation 4x/3x−12 + 3=10

in two equations joined by “and.”

7 answers

To rewrite the equation \( \frac{4x}{3x - 12} + 3 = 10 \) in the form of two equations joined by "and," we can isolate the fraction on one side and the constant on the other.

  1. First, we can rewrite the equation by isolating the fraction: \[ \frac{4x}{3x - 12} = 10 - 3 \]

  2. This simplifies to: \[ \frac{4x}{3x - 12} = 7 \]

Now we can express this as two equations:

  1. The first equation representing the fraction: \[ \frac{4x}{3x - 12} = 7 \]

  2. The second equation representing the simplification: \[ 10 - 3 = 7 \]

Thus, we can write it as: \[ \frac{4x}{3x - 12} = 7 \quad \text{and} \quad 10 - 3 = 7 \]

write the answer with its sybols instaed of the symbols word terms.

Sure! The answer rewritten with symbols is:

\[ \frac{4x}{3x - 12} = 7 \quad \text{and} \quad 10 - 3 = 7 \]

define the meaning of \quad, \text,

In LaTeX, which is the typesetting system used for mathematical notation, \quad and \text{} serve specific purposes:

  1. \quad: This command is used to produce a space of specific width between elements in the document. It creates a space that is roughly equivalent to the width of the letter "M" in the current font (approximately 1 em). It helps in providing visual separation between mathematical expressions or other text for better readability.

    Example:

    • In the expression \( a + b \quad \text{and} \quad c = d \), the \quad creates space around the word "and".

  2. \text{}: This command is used to insert regular text within a mathematical expression. Anything placed inside the {} will be rendered as plain text, adhering to normal text formatting (i.e., it won't be italicized like typical math variables).

    Example:

    • In \( E = mc^2 \quad \text{where} \quad c \text{ is the speed of light} \), the word "where" and the phrase "is the speed of light" are rendered as regular text while maintaining the mathematical notation around it.

Using these commands properly enhances the clarity and aesthetics of mathematical documents prepared in LaTeX.

so really the equation is
4x/3x-12 = 7 and 10 - 3 = 7

Yes, that's correct! The equation can be expressed as:

\[ \frac{4x}{3x - 12} = 7 \quad \text{and} \quad 10 - 3 = 7 \]

This shows that the fraction on the left is equal to 7, and it states that \(10 - 3\) is also equal to 7.