IDNLearn.com provides a reliable platform for finding accurate and timely answers. Our community is here to provide detailed and trustworthy answers to any questions you may have.
Sagot :
To solve for [tex]\( x \)[/tex] so that [tex]\( A \parallel B \)[/tex], we need to understand that parallel lines have the same slope.
Let's go through this step-by-step:
1. Identify the equations:
- The equation for line [tex]\( A \)[/tex] is given as [tex]\( 3x + 20 \)[/tex].
2. Equation for line [tex]\( B \)[/tex]:
- Since we need line [tex]\( B \)[/tex] to be parallel to line [tex]\( A \)[/tex], and parallel lines have the same slope, the general form for line [tex]\( B \)[/tex] would also have the same slope as line [tex]\( A \)[/tex], but possibly a different y-intercept. Thus, if we denote the line [tex]\( B \)[/tex] in the form [tex]\( 3x + k \)[/tex].
3. Setting up the equation:
- To solve for [tex]\( x \)[/tex], we need to set the equation of [tex]\( A \)[/tex] equal to the equation of [tex]\( B \)[/tex]. Since both lines are parallel, their equations would intersect when they are set equal to each other:
[tex]\[ 3x + 20 = 3x + k \][/tex]
4. Solving for [tex]\( x \)[/tex]:
- Simplifying the equation [tex]\( 3x + 20 = 3x + k \)[/tex]:
[tex]\[ \begin{align*} 3x + 20 &= 3x + k \\ 20 &= k \end{align*} \][/tex]
- The above equation holds true regardless of [tex]\( x \)[/tex]. To find a specific value for [tex]\( x \)[/tex], we rearrange the equation:
[tex]\[ 3x = k - 20 \][/tex]
[tex]\[ x = \frac{k - 20}{3} \][/tex]
Therefore, the value of [tex]\( x \)[/tex] that makes lines [tex]\( A \)[/tex] and [tex]\( B \)[/tex] parallel is:
[tex]\[ x = \frac{k}{3} - \frac{20}{3}. \][/tex]
Let's go through this step-by-step:
1. Identify the equations:
- The equation for line [tex]\( A \)[/tex] is given as [tex]\( 3x + 20 \)[/tex].
2. Equation for line [tex]\( B \)[/tex]:
- Since we need line [tex]\( B \)[/tex] to be parallel to line [tex]\( A \)[/tex], and parallel lines have the same slope, the general form for line [tex]\( B \)[/tex] would also have the same slope as line [tex]\( A \)[/tex], but possibly a different y-intercept. Thus, if we denote the line [tex]\( B \)[/tex] in the form [tex]\( 3x + k \)[/tex].
3. Setting up the equation:
- To solve for [tex]\( x \)[/tex], we need to set the equation of [tex]\( A \)[/tex] equal to the equation of [tex]\( B \)[/tex]. Since both lines are parallel, their equations would intersect when they are set equal to each other:
[tex]\[ 3x + 20 = 3x + k \][/tex]
4. Solving for [tex]\( x \)[/tex]:
- Simplifying the equation [tex]\( 3x + 20 = 3x + k \)[/tex]:
[tex]\[ \begin{align*} 3x + 20 &= 3x + k \\ 20 &= k \end{align*} \][/tex]
- The above equation holds true regardless of [tex]\( x \)[/tex]. To find a specific value for [tex]\( x \)[/tex], we rearrange the equation:
[tex]\[ 3x = k - 20 \][/tex]
[tex]\[ x = \frac{k - 20}{3} \][/tex]
Therefore, the value of [tex]\( x \)[/tex] that makes lines [tex]\( A \)[/tex] and [tex]\( B \)[/tex] parallel is:
[tex]\[ x = \frac{k}{3} - \frac{20}{3}. \][/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.