Answered

\begin{tabular}{|c|c|c|c|c|}
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Very warm & Warm & Cold & Cool & Clouded \\
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Partly \\
clouded
\end{tabular} & Clean air & \begin{tabular}{c}
Dry \\
conditions
\end{tabular} & \begin{tabular}{c}
Wet \\
conditions
\end{tabular} & Windy \\
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\end{tabular}

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Day 1 & Date & Forecast & Minimum & Maximum & Description \\
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\end{tabular}



Answer :

GinnyAnswer
Let's work through the problem step by step.

We are given certain expressions and need to perform algebraic manipulations to find the value of the variable [tex]\( a \)[/tex].

### Step-by-Step Solution

1. Define Variables:
- [tex]\( a = 4 \)[/tex]
- [tex]\( b = 9 \)[/tex]

2. Form Expressions:
- Left Expression: [tex]\( 18 - 3a \)[/tex]
- Right Expression: [tex]\( b(a + 1) \)[/tex]

3. Calculate Each Side Separately:
- Substitute [tex]\( a \)[/tex] into the left expression:
[tex]\[ \text{Left Side} = a \cdot (18 - 3a) \][/tex]
Substitute [tex]\( a = 4 \)[/tex]:
[tex]\[ \text{Left Side} = 4 \cdot (18 - 3 \cdot 4) = 4 \cdot 6 = 24 \][/tex]

- Substitute [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the right expression:
[tex]\[ \text{Right Side} = b \cdot (a + 1) \][/tex]
Substitute [tex]\( b = 9 \)[/tex] and [tex]\( a = 4 \)[/tex]:
[tex]\[ \text{Right Side} = 9 \cdot (4 + 1) = 9 \cdot 5 = 45 \][/tex]

4. Combine Like Terms:
- Set up the equation:
[tex]\[ 72 - 12a - (9a + 9) = 0 \][/tex]
Simplify:
[tex]\[ 72 - 12a - 9a - 9 = 0 \][/tex]
Combine like terms:
[tex]\[ 72 - 21a - 9 = 0 \][/tex]
Further simplify:
[tex]\[ 63 - 21a = 0 \][/tex]

5. Solve for [tex]\( a \)[/tex]:
- Isolate [tex]\( a \)[/tex]:
[tex]\[ -21a + 63 = 0 \][/tex]
Move the constant term to the right side:
[tex]\[ -21a = -63 \][/tex]
Solve for [tex]\( a \)[/tex]:
[tex]\[ a = \frac{-63}{-21} = 3 \][/tex]

### Conclusion

We determined that the value for [tex]\( a \)[/tex] is [tex]\( 3 \)[/tex].