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Let us try to formulate the expressions one by one.
let the number be x.
Step 1:
six time the number is 6*x = 6x
Step 2:
product of the number and -3 is -3x
Step 3:
now let us make equation for it:
adding 3x on the left side,
dividing right side by 9
x=45/9 = 5
So the number is x=5
Answer:
see explanation
Step-by-step explanation:
Given
9n² - n - = 0 ← multiply through by 3 to clear the fraction
27n² - 3n - 2 = 0 ← factoring
Consider the factors of the product of the n² term and the constant term which sum to give the coefficient of the n- term
product = 27 × - 2 = - 54 and sum = - 3
The factors are - 9 and + 6
Use these factors to split the n- term
27n² - 9n + 6n - 2 = 0 ( factor the first/second and third/fourth terms )
9n(3n - 1) + 2(3n - 1) = 0 ← factor out (3n - 1) from each term
(3n - 1)(9n + 2) = 0
Equate each factor to zero and solve for n
3n - 1 = 0 ⇒ 3n = 1 ⇒ n =
9n + 2 = 0 ⇒ 9n = - 2 ⇒ n = -