Questions: Solve. Be sure to check. 4(t-1)-5(5t-1)=2-8(6t+1) The answer is (Type an integer or a simplified fraction.)

$Solve. Be sure to check. 4(t-1)-5(5t-1)=2-8(6t+1) The answer is (Type an integer or a simplified fraction.)$

Transcript text: Solve. Be sure to check. \[ 4(t-1)-5(5 t-1)=2-8(6 t+1) \] The answer is $\square$ (Type an integer or a simplified fraction.)

Solution

Solution Steps

Step 1: Distributing and Combining Like Terms

We start with the equation: \[ 4(t-1) - 5(5t-1) = 2 - 8(6t+1) \] Distributing the terms gives us: \[ 4t - 4 - 25t + 5 = 2 - 48t - 8 \] Combining like terms results in: \[ -21t + 1 = -48t - 6 \]

Step 2: Isolating the Variable

Next, we isolate $t$ by moving all terms involving $t$ to one side and constant terms to the other side: \[ -21t + 48t = -6 - 1 \] This simplifies to: \[ 27t = -7 \]

Step 3: Solving for $t$

Now, we solve for $t$ by dividing both sides by 27: \[ t = -\frac{7}{27} \]