Question

Solve each of the following equations and check your results.
1. 5x + 7 = 2x-8
2. 8x +3=27
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Answer 1

Step-by-step explanation:

5x+7=2x−8

3x=−15

x=−5

Factoring: 8x3-27

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3+(a2b-ba2)+(ab2-b2a)-b3 =

a3+0+0+b3 =

a3+b3

Check : 8 is the cube of 2

Check : 27 is the cube of 3

Check : x3 is the cube of x1

Factorization is :

(2x - 3) • (4x2 + 6x + 9)