Chapter 8.2, Problem 73HP

To determine

Evaluate $3\left(2\right)+5$ and solve $3x+5=11$ how the problems and solutions are similar

Answer to Problem 73HP

The problems and solutions are similar because of their results

Explanation of Solution

Given:

The equation $3\left(2\right)+5$ and $3x+5=11$

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 evaluate $3\left(2\right)+5$ the equation as below

  $\begin{array}{c}3\left(2\right)+5\\ =6+5\\ =11\end{array}$

In order to solve the given equation $3x+5=11$ for the variable, isolate the variable term x on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate x on left side, first subtract both sides by $5$ and then divide both sides by $3$ and then simplify further as shown below,

  $\begin{array}{c}3x+5=11\\ 3x+5-5=11-5\\ 3x=6\\ \frac{3x}{3}=\frac{6}{3}\\ x=2\end{array}$

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

Thus, the problems and solutions are similar because of their results