BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.9, Problem 32E
To determine

To calculate: The value of x from the equation 12x3=6+2x by algebraic method and graphical method.

Expert Solution

Answer to Problem 32E

The value of x is 6 and Graph of the equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 32E , additional homework tip  1

Explanation of Solution

Given information:

The equation 12x3=6+2x .

Calculation:

It is provided that the equation 12x3=6+2x .

Algebraic method;

The method in which isolate x on one side of the equation and solve the value of x .

Subtract 2x from the equation 12x3=6+2x ,

  12x2x3=6+2x2x32x3=6

Add 3 in the equation,

  32x3+3=6+332x=9x=6

Therefore, the value of x=6 .

Graphical method;

Let put y1=12x3 and y2=6+2x

The graph of the equation y1=12x3 can be sketched using the table,

    xy1
    03
    22
    41
    24
    45

The graph of equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 32E , additional homework tip  2

The graph of the equation y2=6+2x can be sketched using the table,

    xy2
    06
    210
    414
    22
    42

The graph of equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 32E , additional homework tip  3

The graph of both equations in same figure is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 32E , additional homework tip  4

The solution is the x coordinate of the intersection point (6,6)  of the two graphs. So, the intersection point on the x coordinate is 6 .

Thus, the value of x is 6

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