Question

add. use models if needed.

1. $(4x + 8)+(7x + 3)=$
2. $(-3x + 7)+(-6x + 9)=$
3. $(x - 10)+(3x - 6)=$
4. $(-3x - 7)+(4x + 7)=$
5. $2(x + 14)+(2x - 14)=$
6. $(11x - 8)+7(x - 1)=$
7. 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.
8. 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.
9. find the sum of $(x + 5),(-4x - 2)$, and $(2x - 1)$.

add.

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

Explanation:

Step1: Combine like terms

$$(4x + 8)+(7x + 3)=4x+7x + 8 + 3$$

Step2: Calculate coefficients

$$4x+7x=(4 + 7)x=11x$$

Step3: Calculate constants

$$8 + 3=11$$

Step1: Combine like terms

$$(-3x + 7)+(-6x + 9)=-3x-6x+7 + 9$$

Step2: Calculate coefficients

$$-3x-6x=(-3-6)x=-9x$$

Step3: Calculate constants

$$7 + 9=16$$

Step1: Combine like terms

$$(x-10)+(3x - 6)=x+3x-10-6$$

Step2: Calculate coefficients

$$x+3x=(1 + 3)x=4x$$

Step3: Calculate constants

$$-10-6=-16$$

Step1: Combine like terms

$$(-3x-7)+(4x + 7)=-3x+4x-7 + 7$$

Step2: Calculate coefficients

$$-3x+4x=( - 3+4)x=x$$

Step3: Calculate constants

$$-7 + 7=0$$

Answer:

$$11x+11$$