To solve this problem, we need to find the value of [tex]\(x\)[/tex] in the equation that accurately models the given situation.
The correct linear equation given is:
[tex]\[ 1.95x + 2.50 = 27.46 \][/tex]
Here, [tex]\(1.95x\)[/tex] represents the cost per mile for the taxi, and [tex]\(2.50\)[/tex] is the initial flat fee charged before any miles are driven. The total cost of the trip is [tex]$\$[/tex]27.46[tex]$.
### Step-by-Step Solution:
1. Set up the equation:
\[ 1.95x + 2.50 = 27.46 \]
2. Isolate the variable \(x\):
Subtract the flat fee of \$[/tex]2.50 from both sides of the equation to get the term with [tex]\(x\)[/tex] alone:
[tex]\[ 1.95x + 2.50 - 2.50 = 27.46 - 2.50 \][/tex]
Simplifying, we get:
[tex]\[ 1.95x = 24.96 \][/tex]
3. Solve for [tex]\(x\)[/tex]:
Divide both sides of the equation by the cost per mile which is \$1.95:
[tex]\[ x = \frac{24.96}{1.95} \][/tex]
4. Calculate the value:
Perform the division:
[tex]\[ x = \frac{24.96}{1.95} \approx 12.8 \][/tex]
5. Round to the nearest tenth:
Since 12.8 is already at the nearest tenth, no further rounding is needed.
Therefore, Isaac traveled approximately [tex]\(12.8\)[/tex] miles.
### Conclusion:
The correct answer is:
[tex]\[ 1.95x + 2.50 = 27.46; \text{ Isaac traveled } 12.8 \text{ miles.} \][/tex]
So the correct option from the given choices is:
[tex]\[ 1.95x + 2.50 = 27.46; \text{ Isaac traveled } 12.8 \text{ miles.} \][/tex]
