The difference of a number and -6 is less than 9 write an inequality and solve

n - (-6) < 9

n < 3

Step-by-step explanation:

When setting up an inequality, using the key words from the problem will help.  The word 'difference' would indicate subtraction and 'less than' would be the '<' inequality sign.  Since the expression is 'the difference of a number and -6', we write:  

n - (-6) < 9

Whenever we subtract a negative number, we change both signs to positive:

n + 6 < 9

Using inverse operations to solve:  n + 6 - 6 < 9 - 6

n < 3

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11