Chapter 1.2, Problem 63E

(a)

To determine

To find:whether the value of $x$ is the solution of the given equation.

Answer to Problem 63E

  $x=-1$ is the solution of the given equation.

Explanation of Solution

Given:

  $3x+4=1$ .

Concept used:

A solution to an equation is a value of a variable that makes the equation true. From the statement which value of $x$ satisfies the equation it needs to understand and find the value of $x$ .

By putting the value of variable $x$ if it satisfies the equation then the $x$ is the solution of the equation.

Calculation:

According to the given:

  $3x+4=1$ .

To check if $x=-1$ is the solution of the equation substitute $x=-1$ into the equation.

It can be simplified as:

  $\begin{array}{l}3\left(-1\right)+4=1.\\ \Rightarrow -3+4=1.\\ \Rightarrow 1=1.\end{array}$

Hence, $x=-1$ is the solution of the given equation.

(b)

To determine

To find:whether the value of $x$ is the solution of the given equation.

Answer to Problem 63E

  $x=2$ is not the solution of the given equation.

Explanation of Solution

Given:

  $3x+4=1$ .

Concept used:

A solution to an equation is a value of a variable that makes the equation true. From the statement which value of $x$ satisfies the equation it needs to understand and find the value of $x$ .

By putting the value of variable $x$ if it satisfies the equation then the $x$ is the solution of the equation.

Calculation:

According to the given:

  $3x+4=1$ .

To check if $x=2$ is the solution of the equation substitute $x=2$ into the equation.

It can be simplified as:

  $\begin{array}{l}3\left(2\right)+4=1.\\ \Rightarrow 10\ne 1.\end{array}$

Hence, $x=2$ is not the solution of the given equation.