# How do you solve \frac { x - 4} { 4} = \frac { x - 10} { 10}?

Sep 15, 2017

$10 \left(x - 4\right) = 4 \left(x - 10\right)$

$10 x - 40 = 4 x - 40$

$10 x - 4 x = - 40 + 40$

$6 x = 0$

Ans: $\text{ } x = 0$

#### Explanation:

Step 1: Transposition

$10 \left(x - 4\right) = 4 \left(x - 10\right)$

Step 2: Open brackets

$10 x - 40 = 4 x - 40$

Step 3: Take like terms on one side i.e terms with variable on the left-hand side and rest on the right-hand side

$10 x - 4 x = - 40 + 40$

Step 4: Solve

$6 x = 0$

Step 5: Evaluate for value of $x$

$x = 0$

Answer $\text{ } x = 0$