Question

what is the value of x that makes $ell_1parallelell_2$?
9914 - 1 - page 2

1. what is the value of x that makes $ell_1parallelell_2$?
2. what is the value of x that makes $ell_1parallelell_2$?
3. what is the value of x that makes $ell_1parallelell_2$?

Explanation:

Step1: Use corresponding - angles property

When \(l_1\parallel l_2\), corresponding angles are equal.
For the first pair of lines:
If \(l_1\parallel l_2\), then \(8x=2x + 60\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides:
\(8x-2x=2x + 60-2x\), which simplifies to \(6x=60\).
Divide both sides by 6: \(x = 10\).

For the second pair of lines:

Step1: Use corresponding - angles property

When \(l_1\parallel l_2\), \(8x-14=2x + 54\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(8x-2x-14=2x-2x + 54\), which gives \(6x-14=54\).
Add 14 to both sides: \(6x-14 + 14=54 + 14\), so \(6x=68\).
Divide both sides by 6: \(x=\frac{68}{6}=\frac{34}{3}\).

For the third pair of lines:

Step1: Use corresponding - angles property

When \(l_1\parallel l_2\), \(3x + 17=4x-12\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(3x-3x + 17=4x-3x-12\), which gives \(17=x - 12\).
Add 12 to both sides: \(x=17 + 12=29\).

For the fourth pair of lines:

Step1: Use corresponding - angles property

When \(l_1\parallel l_2\), \(3x-15=2x + 10\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(3x-2x-15=2x-2x + 10\), which gives \(x-15=10\).
Add 15 to both sides: \(x=10 + 15=25\).

Answer:

1. \(x = 10\)
2. \(x=\frac{34}{3}\)
3. \(x = 29\)
4. \(x = 25\)