Question

4-12 practice problems
name:

1. \\(4(x - 3) + (2x + 10)\\)
2. \\((3x + 5) - 2(4x + 7)\\)
3. which expression is not equivalent to \\(22(2 + 3)\\)?

a) \\(22(2) + 22(3)\\) b) \\(22(2)(3)\\) c) \\((2 + 3)(22)\\) d) \\(22(5)\\)

1. find the perimeter of the triangle.
2. find the perimeter above if \\(x = 9\\)
3. find the difference of \\(5(x - 3)\\) and \\((3x + 2)\\)
4. the basketball players will donate \\(20x - 45\\) dollars to a local charity, however the charity needs to collect \\(25x + 10\\) dollars in total, how much more do they need to collect?
5. factor the expressions completely :

(a) \\(12d - 6\\)
gcf:
factored form:
(b) \\(24x + 16y - 4z\\)
gcf:
factored form:
(image of a triangle with sides \\((4x)\\) in, \\((4x)\\) in, \\((13x - 2)\\) in)

Explanation:

Step1: Expand the first term

$4(x-3) = 4x - 12$

Step2: Combine with the second term

$4x - 12 + 2x + 10$

Step3: Combine like terms

$(4x+2x)+(-12+10)=6x-2$

Step1: Expand the second term

$2(4x+7)=8x+14$

Step2: Rewrite the original expression

$3x + 5 - 8x - 14$

Step3: Combine like terms

$(3x-8x)+(5-14)=-5x-9$

Step1: Calculate the original expression

$22(2+3)=22\times5=110$

Step2: Evaluate option a

$22(2)+22(3)=44+66=110$

Step3: Evaluate option b

$22(2)(3)=22\times6=132$

Step4: Evaluate option c

$(2+3)(22)=5\times22=110$

Step5: Evaluate option d

$22(5)=110$

Step1: Sum all side lengths

$4x + 4x + (13x-2)$

Step2: Combine like terms

$(4x+4x+13x)-2=21x-2$

Answer:

$6x-2$

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