Question

Use your knowledge of angle relationships to solve for x in the given expression:

3r−10=2x+30
a) x=2r+10
b) x=3r−40/2
c) x=3r+20/2
d) x=r+5

Answer 1

After isolating x in the equation 3r-10=2x+30 by following several algebraic steps, we find that x equals (3r - 40) / 2. Among the given options, answer choice (c) is closest to the correct answer except for a sign error; the correct equation for x should be 3r - 40 / 2.

Step-by-step explanation:

To solve for x in the expression 3r−10=2x+30, we will first isolate x on one side of the equation. Below are the steps:

1. Subtract 30 from both sides of the equation to get: 3r - 10 - 30 = 2x.
2. Simplify the left side to get: 3r - 40 = 2x.
3. Divide both sides by 2 to solve for x: x = (3r - 40) / 2.

Comparing our solution to the choices given, the correct answer matches option (c), which states x = 3r + 20 / 2. However, there's a minor discrepancy: the plus sign should be a minus sign. The corrected choice would be x = 3r - 40 / 2.