Let's start by looking at the equation \(\frac{7}{8} x + \frac{3}{4} = -6\).
To find another way to express this equation, we might consider changing the fractions to have a common denominator for easier manipulation. However, in this case, instead of converting fractions, let’s focus on simplifying the representation step-by-step.
First, we'll multiply the entire equation by the least common multiple of the denominators to clear the fractions. Here, the denominators we have are 8 and 4, and the least common multiple of 8 and 4 is 8.
Multiply both sides of the equation by 8:
[tex]\[ 8 \left( \frac{7}{8} x + \frac{3}{4} \right) = 8 \cdot (-6) \][/tex]
Distribute the 8 on the left side:
[tex]\[ 8 \cdot \frac{7}{8} x + 8 \cdot \frac{3}{4} = -48 \][/tex]
Since \(8 \cdot \frac{7}{8} = 7\) and \(8 \cdot \frac{3}{4} = 6\), the equation simplifies to:
[tex]\[ 7x + 6 = -48 \][/tex]
This is another way to write the equation [tex]\(\frac{7}{8} x + \frac{3}{4} = -6\)[/tex].
