Chapter 8.2, Problem 49IP

To determine

The solution of the equation $19=3-3d-5d$ , and check the solution.

Answer to Problem 49IP

  $d=-2$

Explanation of Solution

Given:

The equation, $19=3-3d-5d$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation $19=3-3d-5d$ for the unknown variable, isolate the variable term d on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate d on right side, first combining both the d terms and then subtract 3 from both sides and then divide both sides by -8 and then simplify further as shown below,

  $\begin{array}{l}19=3-3d-5d\\ 19=3-8d\\ 19-3=3-8d-3\\ 16=-8d\\ \frac{16}{-8}=\frac{-8d}{-8}\\ -2=d\end{array}$

Thus, the solution of the given equation is $d=-2$ .

Now, to check the solution, substitute $d=-2$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}19=3-3d-5d\\ 19=3-8d\\ 19=3-8\left(-2\right)\\ 19=3+16\\ 19=19\text{True Statement}\end{array}$

Since, the left hand side and right hand side are equal, so the solution is correct.