Question

1. 12x - 4 11x + 3
2. 126° 31x + 2
3. 7x + 3 80°
4. 95° x + 93
5. 9x + 6 11x - 6
6. 120° 20x

find the value of x that makes lines u and v parallel.

1. 7x + 14 9x - 2
2. 7x + 14 9x - 2
3. x + 127 115°
4. x + 103 x + 93
5. 10x + 10 80°

Explanation:

Step1: Use corresponding - angles property

When two lines are parallel, corresponding angles are equal. For example, in problem 10), if the lines are parallel, then \(12x - 4=11x + 3\).

Step2: Solve the equation for \(x\)

Subtract \(11x\) from both sides of the equation \(12x - 4=11x + 3\):
\(12x-11x-4=11x - 11x+3\), which simplifies to \(x-4 = 3\). Then add 4 to both sides: \(x=3 + 4=7\).

For problem 11):

Step1: Use corresponding - angles property

If the lines are parallel, then \(31x+2 = 126\).

Step2: Solve the equation for \(x\)

Subtract 2 from both sides: \(31x=126 - 2=124\). Then divide both sides by 31: \(x=\frac{124}{31}=4\).

For problem 12):

Step1: Use corresponding - angles property

If the lines are parallel, then \(7x + 3=80\).

Step2: Solve the equation for \(x\)

Subtract 3 from both sides: \(7x=80 - 3 = 77\). Then divide both sides by 7: \(x = 11\).

For problem 13):

Step1: Use corresponding - angles property

If the lines are parallel, then \(x + 93=95\).

Step2: Solve the equation for \(x\)

Subtract 93 from both sides: \(x=95 - 93=2\).

For problem 14):

Step1: Use corresponding - angles property

If the lines are parallel, then \(9x+6=11x - 6\).

Step2: Solve the equation for \(x\)

Subtract \(9x\) from both sides: \(6=11x-9x - 6\), which simplifies to \(6 = 2x-6\). Add 6 to both sides: \(2x=6 + 6=12\). Then divide both sides by 2: \(x = 6\).

For problem 15):

Step1: Use corresponding - angles property

If the lines are parallel, then \(20x=120\).

Step2: Solve the equation for \(x\)

Divide both sides by 20: \(x=\frac{120}{20}=6\).

For problem 16):

Step1: Use corresponding - angles property

If the lines are parallel, then \(7x + 14=9x-2\).

Step2: Solve the equation for \(x\)

Subtract \(7x\) from both sides: \(14=9x-7x - 2\), which simplifies to \(14 = 2x-2\). Add 2 to both sides: \(2x=14 + 2=16\). Then divide both sides by 2: \(x = 8\).

For problem 17):

Step1: Use corresponding - angles property

If the lines are parallel, then \(7x + 14=9x-2\) (same as problem 16), and \(x = 8\).

For problem 18):

Step1: Use corresponding - angles property

If the lines are parallel, then \(x + 127=115\).

Step2: Solve the equation for \(x\)

Subtract 127 from both sides: \(x=115 - 127=-12\).

For problem 19):

Step1: Use corresponding - angles property

If the lines are parallel, then \(x + 103=x + 93\), which is a contradiction (\(103
eq93\)), so there is no solution for \(x\) in this case.

For problem 20):

Step1: Use corresponding - angles property

If the lines are parallel, then \(10x+10=80\).

Step2: Solve the equation for \(x\)

Subtract 10 from both sides: \(10x=80 - 10=70\). Then divide both sides by 10: \(x = 7\).

1. \(x = 7\)
2. \(x = 4\)
3. \(x = 11\)
4. \(x = 2\)
5. \(x = 6\)
6. \(x = 6\)
7. \(x = 8\)
8. \(x = 8\)
9. \(x=-12\)
10. No solution
11. \(x = 7\)

Answer:

Step1: Use corresponding - angles property

When two lines are parallel, corresponding angles are equal. For example, in problem 10), if the lines are parallel, then \(12x - 4=11x + 3\).

Step2: Solve the equation for \(x\)

Subtract \(11x\) from both sides of the equation \(12x - 4=11x + 3\):
\(12x-11x-4=11x - 11x+3\), which simplifies to \(x-4 = 3\). Then add 4 to both sides: \(x=3 + 4=7\).

For problem 11):

Step1: Use corresponding - angles property

If the lines are parallel, then \(31x+2 = 126\).

Step2: Solve the equation for \(x\)

Subtract 2 from both sides: \(31x=126 - 2=124\). Then divide both sides by 31: \(x=\frac{124}{31}=4\).

For problem 12):

Step1: Use corresponding - angles property

If the lines are parallel, then \(7x + 3=80\).

Step2: Solve the equation for \(x\)

Subtract 3 from both sides: \(7x=80 - 3 = 77\). Then divide both sides by 7: \(x = 11\).

For problem 13):

Step1: Use corresponding - angles property

If the lines are parallel, then \(x + 93=95\).

Step2: Solve the equation for \(x\)

Subtract 93 from both sides: \(x=95 - 93=2\).

For problem 14):

Step1: Use corresponding - angles property

If the lines are parallel, then \(9x+6=11x - 6\).

Step2: Solve the equation for \(x\)

Subtract \(9x\) from both sides: \(6=11x-9x - 6\), which simplifies to \(6 = 2x-6\). Add 6 to both sides: \(2x=6 + 6=12\). Then divide both sides by 2: \(x = 6\).

For problem 15):

Step1: Use corresponding - angles property

If the lines are parallel, then \(20x=120\).

Step2: Solve the equation for \(x\)

Divide both sides by 20: \(x=\frac{120}{20}=6\).

For problem 16):

Step1: Use corresponding - angles property

If the lines are parallel, then \(7x + 14=9x-2\).

Step2: Solve the equation for \(x\)

Subtract \(7x\) from both sides: \(14=9x-7x - 2\), which simplifies to \(14 = 2x-2\). Add 2 to both sides: \(2x=14 + 2=16\). Then divide both sides by 2: \(x = 8\).

For problem 17):

Step1: Use corresponding - angles property

If the lines are parallel, then \(7x + 14=9x-2\) (same as problem 16), and \(x = 8\).

For problem 18):

Step1: Use corresponding - angles property

If the lines are parallel, then \(x + 127=115\).

Step2: Solve the equation for \(x\)

Subtract 127 from both sides: \(x=115 - 127=-12\).

For problem 19):

Step1: Use corresponding - angles property

If the lines are parallel, then \(x + 103=x + 93\), which is a contradiction (\(103
eq93\)), so there is no solution for \(x\) in this case.

For problem 20):

Step1: Use corresponding - angles property

If the lines are parallel, then \(10x+10=80\).

Step2: Solve the equation for \(x\)

Subtract 10 from both sides: \(10x=80 - 10=70\). Then divide both sides by 10: \(x = 7\).

1. \(x = 7\)
2. \(x = 4\)
3. \(x = 11\)
4. \(x = 2\)
5. \(x = 6\)
6. \(x = 6\)
7. \(x = 8\)
8. \(x = 8\)
9. \(x=-12\)
10. No solution
11. \(x = 7\)