To simplify the expression
[tex]\[ 0.15 (2a - b) + 2 (3b - 4a), \][/tex]
we will follow these steps:
### Step 1: Distribute the constants within each set of parentheses.
1. Distribute [tex]\( 0.15 \)[/tex] in [tex]\( 0.15 (2a - b) \)[/tex]:
[tex]\[ 0.15 \cdot 2a - 0.15 \cdot b = 0.3a - 0.15b. \][/tex]
2. Distribute [tex]\( 2 \)[/tex] in [tex]\( 2 (3b - 4a) \)[/tex]:
[tex]\[ 2 \cdot 3b - 2 \cdot 4a = 6b - 8a. \][/tex]
### Step 2: Combine the resulting terms.
Now, we combine [tex]\( 0.3a - 0.15b \)[/tex] from Step 1 with [tex]\( 6b - 8a \)[/tex]:
[tex]\[ 0.3a - 0.15b + 6b - 8a. \][/tex]
### Step 3: Group and combine like terms.
Combine the terms with [tex]\( a \)[/tex]:
[tex]\[ 0.3a - 8a = -7.7a. \][/tex]
Combine the terms with [tex]\( b \)[/tex]:
[tex]\[ -0.15b + 6b = 5.85b. \][/tex]
### Step 4: Write the simplified expression.
The simplified expression is:
[tex]\[ -7.7a + 5.85b. \][/tex]
So,
[tex]\[ 0.15 (2a - b) + 2 (3b - 4a) \][/tex]
simplifies to:
[tex]\[ -7.7a + 5.85b. \][/tex]
