Question

simplify each variable expression

1. \\(\frac{8x - 5}{-5}\\)
2. \\(-4x + \frac{6x - 10}{2} + 3\\)

Explanation:

Problem 19: Simplify \(\frac{8x - 5}{-5}\)

Step 1: Distribute the denominator

We can split the fraction into two separate fractions: \(\frac{8x}{-5} - \frac{5}{-5}\)

Step 2: Simplify each fraction

Simplify \(\frac{8x}{-5}\) to \(-\frac{8x}{5}\) and \(\frac{5}{-5}\) to \(-1\), so \(-\frac{5}{-5}=1\)
Combining these, we get \(-\frac{8x}{5}+1\)

Problem 21: Simplify \(-4x+\frac{6x - 10}{2}+3\)

Step 1: Simplify the fraction

Simplify \(\frac{6x - 10}{2}\) by dividing each term in the numerator by 2: \(\frac{6x}{2}-\frac{10}{2}=3x - 5\)

Step 2: Combine like terms

Now substitute back into the original expression: \(-4x+(3x - 5)+3\)
Combine the \(x\)-terms: \(-4x + 3x=-x\)
Combine the constant terms: \(-5 + 3=-2\)
So the simplified expression is \(-x - 2\)

Answer:

s:

1. \(\boldsymbol{-\frac{8x}{5}+1}\)
2. \(\boldsymbol{-x - 2}\)