Questions: Solve the equation for (t). [ 0.03(7 t+2)=0.21(t+3)-0.57 ] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (t=) (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. There is no solution.

$Solve the equation for (t). [ 0.03(7 t+2)=0.21(t+3)-0.57 ] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (t=) (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. There is no solution.$

Transcript text: Solve the equation for $t$. \[ 0.03(7 t+2)=0.21(t+3)-0.57 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\mathrm{t}=$ $\square$ (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. There is no solution.

Solution

Solution Steps

To solve the equation $0.03(7t + 2) = 0.21(t + 3) - 0.57$, we will first distribute the constants on both sides of the equation. Then, we will collect all terms involving $t$ on one side and constant terms on the other side. Finally, we will solve for $t$ by isolating it.

Step 1: Distribute and Simplify

We start with the equation: \[ 0.03(7t + 2) = 0.21(t + 3) - 0.57 \] Distributing on both sides gives: \[ 0.21t + 0.06 = 0.21t + 0.63 - 0.57 \] This simplifies to: \[ 0.21t + 0.06 = 0.21t + 0.06 \]

Step 2: Analyze the Equation

Next, we observe that both sides of the equation are identical: \[ 0.21t + 0.06 = 0.21t + 0.06 \] This indicates that the equation holds true for all values of $t$.

Step 3: Conclusion

Since the equation is true for all $t$, we conclude that there are infinitely many solutions.