Question

add. use models if needed. (examples 1-5)

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. (example 6)
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. (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) = $

(the triangle has sides: $(7x + 8)$ mm, $(6x + 6)$ mm, $(9x - 4)$ mm)

Explanation:

Step1: Combine like terms (x terms)

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

Step2: Calculate sums

$11x + 11$

---

Step1: Combine like terms (x terms)

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

Step2: Calculate sums

$-9x + 16$

---

Step1: Combine like terms (x terms)

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

Step2: Calculate sums

$4x - 16$

---

Step1: Combine like terms (x terms)

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

Step2: Calculate sums

$x + 0 = x$

---

Step1: Distribute the coefficient

$2x + 28 + 2x -14$

Step2: Combine like terms

$(2x + 2x) + (28 -14)$

Step3: Calculate sums

$4x + 14$

---

Step1: Distribute the coefficient

$11x -8 + 7x -7$

Step2: Combine like terms

$(11x +7x) + (-8 -7)$

Step3: Calculate sums

$18x -15$

---

Step1: Sum all side lengths

$(7x+8)+(6x+6)+(9x-4)$

Step2: Combine like terms

$(7x+6x+9x)+(8+6-4)$

Step3: Simplify expression

$22x + 10$

Step4: Substitute $x=10$

$22(10) + 10 = 220 + 10$

Step5: Calculate final perimeter

$230$

---

Step1: Use rectangle perimeter formula

$2\times(\text{length} + \text{width}) = 2[(2x-5)+(2x+6)]$

Step2: Simplify inside parentheses

$2[(2x+2x)+(-5+6)] = 2(4x +1)$

Step3: Distribute the coefficient

$8x + 2$

Step4: Substitute $x=12$

$8(12) + 2 = 96 + 2$

Step5: Calculate final perimeter

$98$

---

Step1: Write the sum expression

$(x+5)+(-4x-2)+(2x-1)$

Step2: Combine like terms (x terms)

$(x-4x+2x)+(5-2-1)$

Step3: Calculate sums

$-x + 2$

---

Step1: Combine like terms (x terms)

$(-3.5x +9.1x)+(1.7-0.3)$

Step2: Calculate sums

$5.6x + 1.4$

---

Step1: Combine like terms (x terms)

$(0.5x +8.2x)+(15-16.6)$

Step2: Calculate sums

$8.7x - 1.6$

Answer:

1. $11x + 11$
2. $-9x + 16$
3. $4x - 16$
4. $x$
5. $4x + 14$
6. $18x - 15$
7. Simplified perimeter: $22x + 10$; Perimeter at $x=10$: $230$ mm
8. Simplified perimeter: $8x + 2$; Perimeter at $x=12$: $98$ meters
9. $-x + 2$
10. $5.6x + 1.4$
11. $8.7x - 1.6$