Question

What are the solutions to the absolute value inequality |x − 70| ≤ 3? Remember, the inequality can be written as −3 ≤ x − 70 ≤ 3 or as x − 70 ≤ 3 and x − 70 ≥ −3

Answer 1

67 ≤ x ≤ 73

Explanation:

Given inequality is: |x − 70| ≤ 3

We have to find the value of x.

If |x| ≤ a then x ≤ a and x ≥ -a .

Applying this rule to given inequality,we get x - 70 ≤ 3 and x - 70 ≥ -3

Adding 70 to both sides of above both inequality,we get

x-70+70 ≤ 3+70 and x-70+70 ≥ -3+70

Adding like terms,we get

x ≤ 73 and x ≥ 67

Combining above two inequalities ,we get

67 ≤ x ≤ 73 which is the answer.

Answer 2

solutions to the absolute value inequality is
`67\leq x\leq 73`

Explanation:

To find the solution of x absolute value of |x − 70| ≤ 3 will be written in the form of interval because the given fraction (x-70) is less than and equal to 3.

`-3\leq(x-70)\leq 3`

Now we add 70 on every part of the inequality.

`-3+70\leq (x-70)+70\leq 3+70`

`67\leq x\leq 73`

So the solution to the absolute value inequality is
`67\leq x\leq 73`.