Chapter 1.5, Problem 13PPS

a.

To determine

To write: An equation that says the length of a rectangle is $4$ more than six times the value of $x$ .

Answer to Problem 13PPS

The equation is $y=6x+4$ .

Explanation of Solution

Given Information: Length should be $4$ more than six times the value of $x$ .

Calculation:

Let length of rectangle be $y$ .

For $y$ to be $4$ more than six times the value of $x$ ,

  $y=6x+4$

Thus, the equation is $y=6x+4$ .

b.

To determine

To write: An equation that says the width of a rectangle is $1$ less than three times the value of $x$ .

Answer to Problem 13PPS

The equation is $z=3x-1$

Explanation of Solution

Given Information: Width should be $1$ less than three times the value of $x$ .

Calculation:

Let width of rectangle be $z$ .

For $z$ to be $1$ less than three times the value of $x$ ,

  $z=3x-1$

Thus, the equation is $z=3x-1$ .

c.

To determine

To write: An equation for perimeter of the rectangle.

Answer to Problem 13PPS

Equation for perimeter of rectangle is $96=2(9x+3)$ .

Explanation of Solution

Given Information: Value of perimeter is $96$ .

Calculation:

From previous parts, it is known that, $y$ is length of rectangle and $z$ represents rectangle’s width.

Perimeter of rectangle $=2y+2z$

  $=2(y+z)$

It is given that the value of perimeter is $96$ , substituting the values $y=6x+4$ and $z=3x-1$ (from previous parts)

  $\begin{array}{l}2(6x+4+3x-1)=96\\ 2(9x+3)=96\\ 96=2(9x+3)\end{array}$

Thus, equation for perimeter of rectangle $96=2(9x+3)$ .

d.

To determine

To simplify: The right side of the equation from previous part using distributive property.

Answer to Problem 13PPS

Simplified equation is $96=18x+6$ .

Explanation of Solution

Given Information: Equation $96=2(9x+3)$

Calculation:

  $\begin{array}{l}96=2(9x+3)\\ 96=18x+6\text{Distributive Property}\end{array}$

Thus, simplified equation is $96=18x+6$ .

e.

To determine

To combine: The like terms of the right side of the equation.

Answer to Problem 13PPS

After combining like terms, equation is $18x=90$ .

Explanation of Solution

Given Information: Terms of right side are to be combined

Calculation:

  $\begin{array}{l}96=18x+6\\ 18x=96-6\\ 18x=90\end{array}$

Thus, after combining like terms equation is $18x=90$ .

f.

To determine

To find: The solution $x$ of the equation.

Answer to Problem 13PPS

The solution is $x=5$ .

Explanation of Solution

Given Information: Equation from previous part.

Calculation:

Equation is $18x=90$ .

Solving for $x$ ,

  $\begin{array}{l}18x=90\\ x=\frac{90}{18}\\ x=5\end{array}$

Thus, the solution is $x=5$ .