Answer :
To find the distance between the two lines [tex]$l_1$[/tex] and [tex]$l_2$[/tex], let's go through the problem step-by-step.
1. Write down the equations of the lines:
- Line [tex]\( l_1 \)[/tex] is described by the equation: [tex]\( 24 + x = 3 \)[/tex].
- Line [tex]\( l_2 \)[/tex] is described by the equation: [tex]\( 24 + x = 1 \)[/tex].
2. Solve each equation for [tex]\( x \)[/tex]:
- For line [tex]\( l_1 \)[/tex], solve for [tex]\( x \)[/tex]:
[tex]\[
24 + x = 3 \\
x = 3 - 24 \\
x = -21
\][/tex]
- For line [tex]\( l_2 \)[/tex], solve for [tex]\( x \)[/tex]:
[tex]\[
24 + x = 1 \\
x = 1 - 24 \\
x = -23
\][/tex]
3. Calculate the distance between the lines:
The distance between two vertical lines on the x-axis is the absolute difference between their x-values. Thus, the distance [tex]\( d \)[/tex] between [tex]\( l_1 \)[/tex] and [tex]\( l_2 \)[/tex] is:
[tex]\[
d = \left| x_{l_2} - x_{l_1} \right| \\
d = \left| -23 - (-21) \right| \\
d = \left| -23 + 21 \right| \\
d = \left| -2 \right| \\
d = 2
\][/tex]
Thus, the distance between line [tex]\( l_1 \)[/tex] and line [tex]\( l_2 \)[/tex] is 2 units.
1. Write down the equations of the lines:
- Line [tex]\( l_1 \)[/tex] is described by the equation: [tex]\( 24 + x = 3 \)[/tex].
- Line [tex]\( l_2 \)[/tex] is described by the equation: [tex]\( 24 + x = 1 \)[/tex].
2. Solve each equation for [tex]\( x \)[/tex]:
- For line [tex]\( l_1 \)[/tex], solve for [tex]\( x \)[/tex]:
[tex]\[
24 + x = 3 \\
x = 3 - 24 \\
x = -21
\][/tex]
- For line [tex]\( l_2 \)[/tex], solve for [tex]\( x \)[/tex]:
[tex]\[
24 + x = 1 \\
x = 1 - 24 \\
x = -23
\][/tex]
3. Calculate the distance between the lines:
The distance between two vertical lines on the x-axis is the absolute difference between their x-values. Thus, the distance [tex]\( d \)[/tex] between [tex]\( l_1 \)[/tex] and [tex]\( l_2 \)[/tex] is:
[tex]\[
d = \left| x_{l_2} - x_{l_1} \right| \\
d = \left| -23 - (-21) \right| \\
d = \left| -23 + 21 \right| \\
d = \left| -2 \right| \\
d = 2
\][/tex]
Thus, the distance between line [tex]\( l_1 \)[/tex] and line [tex]\( l_2 \)[/tex] is 2 units.
