Solve the equation 14 - 4(t - 5) = 10 - t.

Step-by-step solution

1. 1

   Distribute −4 across the bracket, watching the second sign. The factor is $-4$, not $4$, so it multiplies both terms inside:

   $-4(t-5) = -4t + 20$

   The $+20$ comes from $(-4)(-5)$. Writing $-20$ here is the single most common error in this type of equation.

2. 2

   Combine the constants on the left.

   $14 - 4t + 20 = 34 - 4t \quad\Longrightarrow\quad 34 - 4t = 10 - t$

3. 3

   Collect the variable terms on the side that keeps the coefficient positive. Adding $4t$ to both sides:

   $34 = 10 + 3t$

4. 4

   Isolate and divide.

   $24 = 3t \quad\Longrightarrow\quad t = 8$

5. 5

   Verify in the original equation. Left: $14 - 4(8 - 5) = 14 - 4(3) = 14 - 12 = 2$. Right: $10 - 8 = 2$. Both sides equal $2$, so $t = 8$ is correct.