Question

do not put space between the characters. example: 3x+4 or 1/2x - 3 simplify: 1. $n + 4 - 9 - 5n$ 2. $7x - 4y - 8 - 3x$ 3. $18 - 2(4x + 7)+5x$ 4. $9(x - 3)-(x + )$ 5. write the perimeter of the triangle in simplest form. 6. write the perimeter of rectangle in simplest form.

Explanation:

Step1: Combine like - terms for 1.

$n+4 - 9-5n=(n - 5n)+(4 - 9)=-4n - 5$

Step2: Combine like - terms for 2.

$7x-4y - 8-3x=(7x - 3x)-4y - 8 = 4x-4y - 8$

Step3: Expand and combine like - terms for 3.

First expand $2(4x + 7)=8x+14$. Then $18-2(4x + 7)+5x=18-(8x + 14)+5x=18 - 8x-14 + 5x=(18 - 14)+(-8x+5x)=4 - 3x$

Step4: Expand and combine like - terms for 4.

Expand $9(x - 3)=9x-27$ and $-(x + 2)=-x - 2$. Then $9(x - 3)-(x + 2)=9x-27-x - 2=(9x - x)+(-27 - 2)=8x-29$

Step5: Find the perimeter of the triangle.

The perimeter $P$ of a triangle with side lengths $a = 2x-6$, $b = 3x + 1$, and $c=x + 8$ is $P=(2x-6)+(3x + 1)+(x + 8)=(2x+3x+x)+(-6 + 1+8)=6x + 3$

Step6: Find the perimeter of the rectangle.

Assume the length $l = 2v+13$ and width $w$ is not given. If we assume it's a square - like case (a special rectangle) or the other side is also $2v+13$, the perimeter $P = 2(2v+13)+2(2v+13)=4(2v+13)=8v + 52$

Answer:

1. $-4n - 5$
2. $4x-4y - 8$
3. $4 - 3x$
4. $8x-29$
5. $6x + 3$
6. $8v + 52$