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renknee

Answer:

Last option; x < 2 and x > -1

Step-by-step 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.

  • [tex]2x - 1 + 1 < 3 + 1[/tex]
  • [tex]2x < 4[/tex]

Step 2: Divide both sides by 2.

  • [tex]\frac{2x}{2} < \frac{4}{2}[/tex]
  • [tex]x < 2[/tex]  

3. (Solving for 2nd condition)

Step 1: Add 1 to both sides.

  • [tex]2x - 1 + 1 > -3 + 1[/tex]
  • [tex]2x > -2[/tex]

Step 2: Divide both sides by 2.

  • [tex]\frac{2x}{2} > \frac{-2}{2}[/tex]
  • [tex]x > -1[/tex]

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:

Ver imagen renknee

Answer:

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.

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