To combine like terms in the expression
[tex]\[ \frac{9}{8} m + \frac{9}{10} - 2 m - \frac{3}{5}, \][/tex]
we need to separate the terms involving [tex]\( m \)[/tex] from the constant terms and then combine them separately.
Step 1: Combine the coefficients of [tex]\( m \)[/tex] terms
- The coefficients of [tex]\( m \)[/tex] in the expression are [tex]\( \frac{9}{8} \)[/tex] and [tex]\( -2 \)[/tex].
1. Convert all coefficients to a common base:
[tex]\( \frac{9}{8} \)[/tex] is already a fraction.
Represent [tex]\( -2 \)[/tex] as a fraction with the same denominator:
[tex]\[ -2 = -2 \cdot \frac{8}{8} = \frac{-16}{8}. \][/tex]
2. Combine the coefficients:
[tex]\[ \frac{9}{8} + \frac{-16}{8} = \frac{9 - 16}{8} = \frac{-7}{8}. \][/tex]
So, the combined [tex]\( m \)[/tex] term is:
[tex]\[ \frac{-7}{8} m. \][/tex]
Step 2: Combine the constant terms
- The constant terms in the expression are [tex]\( \frac{9}{10} \)[/tex] and [tex]\( -\frac{3}{5} \)[/tex].
1. Convert all constants to a common denominator:
The least common denominator for 10 and 5 is 10.
[tex]\[ -\frac{3}{5} = -\frac{3 \cdot 2}{5 \cdot 2} = -\frac{6}{10}. \][/tex]
2. Combine the constant terms:
[tex]\[ \frac{9}{10} + \left(-\frac{6}{10}\right) = \frac{9 - 6}{10} = \frac{3}{10}. \][/tex]
Therefore, the combined constant term is:
[tex]\[ \frac{3}{10}. \][/tex]
Step 3: Combine all terms
The final equivalent expression, after combining like terms, is:
[tex]\[ \frac{-7}{8} m + \frac{3}{10}. \][/tex]
For clarity, we can present the results as numerical values:
The coefficient of [tex]\( m \)[/tex] is [tex]\[-0.875\][/tex] (since [tex]\(\frac{-7}{8} \approx -0.875\)[/tex]).
The constant term is [tex]\[-0.3\][/tex] (since [tex]\(0.3\)[/tex] approximates to [tex]\(\frac{3}{10}\)[/tex]).
Hence, the simplified expression combining like terms is:
[tex]\[ \boxed{-0.875 m - 0.3}. \][/tex]
