Chapter 8, Problem 54CR

To determine

The solution of the equation $5+3y=3\left(2+y\right)$ ,

Answer to Problem 54CR

  $0$

Explanation of Solution

Given:

The equation, $5+3y=3\left(2+y\right)$

Concept Used:

Left distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

• 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 $5+3y=3\left(2+y\right)$ for the variable, isolate the variable term y on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate y on left side, first use Left distributive property and then subtract both sides by $5$ and then subtract both sides by $3y$ and then simplify further as shown below,

  $\begin{array}{c}5+3y=3\left(2+y\right)\\ 5+3y=3\cdot 2+3\cdot y\\ 5+3y=6+3y\\ 5+3y-5=6+3y-5\\ 3y=3y+1\\ 3y-3y=3y+1-3y\\ 0\end{array}$

Thus, the solution of the given equation is $0$ .

Now in order to check the solution of the equation, substitute $y=0$ in the given equation and check whether the left hand side and right hand side are equal. So, it gives

  $\begin{array}{c}5+3y=3\left(2+y\right)\\ 5+3\left(0\right)=3\left(2+0\right)\\ 5+0=6\\ 5=6\text{False statement}\end{array}$

Thus, the solution of the given equation is $y=0$ .