Question

simplify the expression.

\\\frac{4}{5}(5x - 10) - \frac{3}{4}(12 + 4x)\\

a. \\(x - 17\\)
b. \\(7x - 17\\)
c. \\(7x - 1\\)
d. \\(8x - 19\\)

Explanation:

⚡ Using what you learned: using properties of operations

Step 1: Distribute the first fraction

Multiply \( \frac{4}{5} \) by each term inside the first set of parentheses:

$$ \frac{4}{5}(5x) - \frac{4}{5}(10) = 4x - 8 $$

Step 2: Distribute the second fraction

Multiply \( -\frac{3}{4} \) by each term inside the second set of parentheses:

$$ -\frac{3}{4}(12) - \frac{3}{4}(4x) = -9 - 3x $$

Step 3: Combine like terms

Group and combine the \( x \)-terms and the constant terms:

$$ (4x - 3x) + (-8 - 9) = x - 17 $$

Answer:

A \( x - 17 \)