Solve the equation 6(x - 5) = 7(x - 1).

Step-by-step solution

1. 1

   Expand both brackets. Each outside factor multiplies both terms inside:

   $6x - 30 = 7x - 7$

2. 2

   Decide which side keeps the variable. The coefficient on the right, $7$, is larger than the $6$ on the left, so moving the $x$ terms right avoids a negative coefficient. Subtract $6x$ from both sides:

   $-30 = x - 7$

3. 3

   Move the constant. Adding $7$ to both sides:

   $-30 + 7 = x \quad\Longrightarrow\quad x = -23$

4. 4

   Check by substitution. Left: $6(-23 - 5) = 6(-28) = -168$. Right: $7(-23 - 1) = 7(-24) = -168$. Both sides equal $-168$.

5. 5

   Note why the root is so far from zero. The two lines $y = 6x - 30$ and $y = 7x - 7$ have nearly equal slopes ($6$ and $7$) but constants $23$ apart, so they meet a long way to the left of the origin — the smaller the slope gap, the further out the intersection.