Question: If $10 + 2(t - 16) = t - 2(t - 5)$, then $t = \underline{\hspace{1cm}}$ $\circ \quad 9.00$…

If $10 + 2(t - 16) = t - 2(t - 5)$, then $t = \underline{\hspace{1cm}}$

$\circ \quad 9.00$

$\circ \quad 5.33$

$\circ \quad 3.67$

$\circ \quad 6.40$

$\circ \quad 10.67$

Solution

The given equation is: \[ 10 + 2(t - 16) = t - 2(t - 5) \] First, distribute the terms: \[ 10 + 2t - 32 = t - 2t + 10 \] Simplify each side: \[ 2t - 22 = -t + 10 \] Add \(t\) to both sides: \[ 3t - 22 = 10 \] Add 22 to both sides: \[ 3t = 32 \] Divide by 3: \[ t = \frac{32}{3} \] Solve: \[ t = 10.67 \] So, the value of \( t \) is 10.67.