Answer:
x = 26
Step-by-step explanation:
1. First, we should realize that the angle with 5x + 7 and the angle with 8x - 71 are alternate exterior angles, so they're congruent.
- This means that 5x + 7 = 8x - 71
2. (Solving)
Step 1: Subtract 8x from both sides.
- [tex]5x + 7 - 8x = 8x - 71 - 8x[/tex]
- [tex]-3x + 7 =-71[/tex]
Step 2: Subtract 7 from both sides.
- [tex]-3x + 7 - 7 = -71 - 7[/tex]
- [tex]-3x = -78[/tex]
Step 3: Divide both sides by -3.
- [tex]\frac{-3x}{-3}=\frac{-78}{-3}[/tex]
- [tex]x = 26[/tex]
Step 4: Check if solution is correct.
- [tex]5(26)+7=9(26)-71[/tex]
- [tex]130 + 7 = 208 - 71[/tex]
- [tex]137 = 137[/tex]
Therefore, x = 26.
