Chapter 1.1, Problem 31E

To determine

To solve the equation

  $\frac{3}{2}+t=\frac{1}{2}$

Answer to Problem 31E

  $t=-1$ is the solution.

Explanation of Solution

Given: Equation: $\frac{3}{2}+t=\frac{1}{2}$

Formula Used:

The subtraction property of equality tells us that if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same.

Calculation:

Given: Equation: $\frac{3}{2}+t=\frac{1}{2}$

To solve the equation, Subtracting $\frac{3}{2}$ from both the sides as “Subtraction property of equality tells us that if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same”

  $\begin{array}{l}\frac{3}{2}+t-\frac{3}{2}=\frac{1}{2}-\frac{3}{2}\\ t=\frac{1-3}{2}\\ t=\frac{-2}{2}\\ t=-1\end{array}$

Thus, the solution is $t=-1$ .

Now, putting the value of $t=-1$ in the L.H.S. of the equation, we have:

  $\begin{array}{l}\frac{3}{2}-1=\frac{3-2}{2}\\ \frac{3}{2}-1=\frac{1}{2}\end{array}$

And R.H.S. of the equation is $\frac{1}{2}$ .

Hence, L.H.S. $=$ R.H.S.

Thus, the solution is correct.

Conclusion:

Hence, the solution is $t=-1$ .