Question

Question

Solve for and graph the solution on the number line below.
2x−1≤−21or
1<2x−1

Answer 1

To solve the inequality 2x - 1 ≤ -21, we can start by isolating the variable x.
Adding 1 to both sides of the inequality gives:
2x ≤ -20

Next, divide both sides of the inequality by 2 to solve for x:
x ≤ -10

To solve the inequality 1 < 2x - 1, we can start by isolating the variable x.
Adding 1 to both sides of the inequality gives:
2 < 2x

Divide both sides of the inequality by 2 to solve for x:
1 < x

Now, we can graph the solutions on the number line.

On the number line, mark the point -10 with a closed circle, as x can be equal to -10. Then, shade the line to the left of -10 to represent all the values of x that are less than or equal to -10.

Next, mark the point 1 with an open circle, as x cannot be equal to 1. Then, shade the line to the right of 1 to represent all the values of x that are greater than 1.

The graph on the number line would look like this:

-----·---´-----------------------------------·----->
-10 1

The shaded region to the left of -10 and the shaded region to the right of 1 represent the solutions to the given inequalities.

Answer 2

solve for x

Answer 3

To solve for x, we can consider both inequalities separately:

For 2x - 1 ≤ -21:
Adding 1 to both sides, we get:
2x ≤ -20
Dividing both sides by 2:
x ≤ -10

For 1 < 2x - 1:
Adding 1 to both sides, we get:
2x > 2
Dividing both sides by 2:
x > 1

So the solution for the inequalities is:
x ≤ -10 or x > 1

Graphically, on the number line, we can represent this solution as:

-----·----------------´-·------------------·------>
-10 1

The shaded region to the left of -10 and the open circle at 1 represent the solution to the inequalities.