# Algebra

posted by .

Solve the inequality and express the solution in terms of intervals whenever possible.

| x+3 | < 0.01

I know the answer is : (-3.01,-2.99)

Please show me how to solve this type of math problem.

• Algebra -

The absolute value actually represents two cases, the contents are positive (in which case the absolute value does not do much), or if the contents are negative, then the negative sign is dropped.

Mathematically speaking, the above equation can be broken down to two:

x+3 < 0.01 ....(1)

and

-(x+3) < 0.01 ...(2)

Solving (1) gives us
x < 0.01-3 = 2.99, or
x<-2.99

Solving (2) gives us
-(x+3)<0.01
-x-3<0.01
x>-3-0.01=-3.01
So together, we have
x ∈ (-3.01,-2.99)

## Similar Questions

1. ### Algebra

Solve. (x+5)(x-3)(x+4) is greater than 0. Use at least one inequality or compound inequality to express your answer. Type R if the answer is in all real numbers.

Solve (x+17)(x-20)(x+8)>0 The solution set is (x )?
3. ### Calc 1 - Factoring??

Solve the inequality. Express the solution sets as intervals or unions of intervals and show them on the real line. Use the result (square-root of a^2) = |a| as appropriate. (x+3)^2 < 2
4. ### Algebra 1A

could someone please help and check my answer thank you. simplify your answer, type an inequality symbol, then type an integer or a decimal solve 7 x + 2 <30 the solution is {x[< 30}, 0.30 is this correct?
5. ### Solve Inequality

Solve the inequality. Express your solution using interval notation and please show all of your work. x(x + 6)(8 – x) >= 0 I need help, I guess I'm not understanding the interval notation portion. I know, that when 0 <= x <= …
6. ### Math - Problem4

Solve the inequality. Express your solution using interval notation and please show all of your work. x^4 - 7x^2 - 14 > 0