Questions: Simplify each expression: (a) 9k - 2(k+6) + 8k = (b) 5/12 z - 7/8 + 5/6 z - 3/5 =

Solution Steps

To simplify each expression, we will combine like terms. For expression (a), we will distribute the -2 across the terms inside the parentheses and then combine the resulting like terms. For expression (b), we will find a common denominator for the fractions and then combine the terms.

We start with the expression \( 9k - 2(k + 6) + 8k \). First, we distribute the \(-2\) across the terms inside the parentheses:

\[ 9k - 2k - 12 + 8k \]

Next, we combine the like terms:

\[ (9k - 2k + 8k) - 12 = 15k - 12 \]

For the second expression \( \frac{5}{12}z - \frac{7}{8} + \frac{5}{6}z - \frac{3}{5} \), we first find a common denominator for the fractions. The least common multiple of \(12\), \(8\), and \(5\) is \(120\). We rewrite each term with this common denominator:

\[ \frac{5}{12}z = \frac{50}{120}z, \quad \frac{5}{6}z = \frac{100}{120}z, \quad \frac{7}{8} = \frac{105}{120}, \quad \frac{3}{5} = \frac{72}{120} \]

Now substituting these back into the expression gives:

\[ \frac{50}{120}z - \frac{105}{120} + \frac{100}{120}z - \frac{72}{120} \]

Combining the \(z\) terms and the constant terms:

\[ \left(\frac{50}{120}z + \frac{100}{120}z\right) - \left(\frac{105}{120} + \frac{72}{120}\right) = \frac{150}{120}z - \frac{177}{120} \]

This simplifies to:

\[ \frac{5}{4}z - \frac{59}{40} \]

Final Answer