the value of x in the diagram is 6.
From the diagram, we can see that two sides of a triangle are labeled:
Side BD: 9x - 35
Side AC: 2x + 7
We are also given that these two sides are equal in length. Therefore, we can write the following equation:
9x - 35 = 2x + 7
Step 2: Solve the linear equation
We can solve the equation for x using simple algebraic operations. Here's how we do it:
Add 35 to both sides:
9x = 2x + 42
Subtract 2x from both sides:
7x = 42
Divide both sides by 7:
x = 6
Therefore, the value of x in the diagram is 6.