Solve: |4x + 2| < 8 help me please

-5/2 < x < 3/2

In interval notation: (-5/2, 3/2)

Step-by-step explanation:

Rule

To solve an absolute value inequality of the form

|X| < k

where X is an expression in x and k is a non-negative number,

solve the following compound inequality

-k < X < k

For this problem, X is 4x + 2, an expression in x. k is 8.

Follow the rule above, and change the absolute value inequality

|4x + 2| < 8 into

-8 < 4x + 2 < 8

Now we solve the compound inequality.

Subtract 2 from the three sides.

-10 < 4x < 6

Divide the three sides by 4.

-10/4 < x < 6/4

Reduce the fractions.

-5/2 < x < 3/2

-5/2 < x < 3/2

In interval notation: (-5/2, 3/2)

or

Step-by-step explanation:

To get the fraction

answer: give more info

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: