Question

1. write a linear expression in simplest form to represent the perimeter of the triangle at the right. then find the perimeter if the value of x is 10 millimeters. (example 6)
2. a rectangle has side lengths (2x - 5) meters and (2x + 6) meters. write a linear expression in simplest form to represent the perimeter. find the perimeter if the value of x is 12 meters. (example 6)

9 find the sum of (x + 5), (-4x - 2), and (2x - 1).
add.

1. (-3.5x + 1.7) + (9.1x - 0.3) =
2. (0.5x + 15) + (8.2x - 16.6) =

lesson 6 add linear expressions 399

Explanation:

Problem 7

Step1: Find the perimeter expression

The perimeter \(P\) of a triangle is the sum of its side lengths.
\(P=(7x + 8)+(6x + 6)+(9x-4)\)
Combine like - terms:

$$
LATEXBLOCK0
$$

Step2: Substitute \(x = 10\)

When \(x = 10\), \(P=22\times10+10\)
\(P=220 + 10=230\)

Step1: Use the rectangle perimeter formula \(P = 2(l + w)\)

Here \(l=(2x + 6)\) and \(w=(2x-5)\)
\(P=2[(2x + 6)+(2x-5)]\)
First, simplify the expression inside the brackets: \((2x+6)+(2x - 5)=4x+1\)
Then \(P = 2(4x + 1)=8x+2\)

Step2: Substitute \(x = 12\)

When \(x = 12\), \(P=8\times12+2\)
\(P=96+2 = 98\)

Step1: Find the sum

\((x + 5)+(-4x-2)+(2x-1)\)
Combine like - terms:

$$
LATEXBLOCK0
$$

Answer:

The linear expression for the perimeter is \(22x + 10\) mm. When \(x = 10\), the perimeter is \(230\) mm.

Problem 8