Let's solve the problem step by step to determine how many miles Marcus biked.
The problem states:
- Jenny biked 3 miles less than twice the number of miles Marcus biked.
- Jenny biked a total of 4 miles.
Let [tex]\( x \)[/tex] represent the number of miles Marcus biked.
Since Jenny biked 3 miles less than twice the number of miles Marcus biked, we can write an equation based on this description:
[tex]\[ 2x - 3 = 4 \][/tex]
This equation represents the situation as follows:
- [tex]\( 2x \)[/tex] represents twice the number of miles Marcus biked.
- Subtracting 3 from [tex]\( 2x \)[/tex] accounts for the "3 miles less".
- The right side of the equation, 4, represents the total miles Jenny biked.
To solve for [tex]\( x \)[/tex]:
1. Add 3 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 2x - 3 + 3 = 4 + 3 \][/tex]
[tex]\[ 2x = 7 \][/tex]
2. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{7}{2} \][/tex]
[tex]\[ x = 3.5 \][/tex]
Therefore, Marcus biked 3.5 miles.
Among the given multiple-choice options, the correct equation is:
[tex]\[ 4 = 2x - 3 \][/tex]
