Given that 𝑥−1:5𝑥−14=1:2find the value of 𝑥.

Sure, let's solve the equation step by step.

The given equation is 𝑥−1:5𝑥−14=1:2.

This is a ratio equation, and it can be solved like a normal equation.

Step 1: Convert the ratios into fractions. So, the equation becomes (𝑥−1)/(5𝑥−14) = 1/2.

Step 2: Cross multiply the fractions. This gives 2*(𝑥−1) = 1*(5𝑥−14).

Step 3: Simplify the equation. This gives 2𝑥 - 2 = 5𝑥 - 14.

Step 4: Rearrange the equation to get all the x terms on one side and the numbers on the other. This gives 5𝑥 - 2𝑥 = 14 + 2.

Step 5: Simplify the equation. This gives 3𝑥 = 16.

Step 6: Finally, solve for 𝑥 by dividing both sides of the equation by 3. This gives 𝑥 = 16/3.

So, the value of 𝑥 is 16/3.