Question

ABSOLUTEEE VALUEEEE HELPP PLZ

Answer 1

We solve first:

l 2x - 1 I < 3

2x - 1 < 3

(inverse property of subtraction is addition)

+1 +1 *adding 1 to both sides to isolate the variable*

2x < 4

Inverse property of multiplication is division so:

/2 /2 dividing by 2 to isolate the variable

X < 2

Now let's find the numberline that says so.

Let's choose D since the numberline is at -1 we can let that be X, which is below positive two since the other part of the numberline is at 2 showing that X is less than 2.

Answer 2

Last option; x < 2 and x > -1

Explanation:

1. We know 2x − 1 < 3 and 2x − 1 > −3, so let's solve both of these inequalities.

2. (Solving for 1st condition)

Step 1: Add 1 to both sides.

• 
  `2x - 1 + 1 < 3 + 1`
• 
  `2x < 4`

Step 2: Divide both sides by 2.

• 
  `(2x)/(2) < (4)/(2)`
• 
  `x < 2`

3. (Solving for 2nd condition)

Step 1: Add 1 to both sides.

• 
  `2x - 1 + 1 > -3 + 1`
• 
  `2x > -2`

Step 2: Divide both sides by 2.

• 
  `(2x)/(2) > (-2)/(2)`
• 
  `x > -1`

4. Now, we know that the value of x is greater than -1 but less than 2, and we can represent it on a number line like this: