-2<2x+1 3 -4 <1
To solve the inequality -2 < 2x + 1, we need to isolate the variable x.
First, we subtract 1 from both sides of the inequality:
-2 - 1 < 2x + 1 - 1
-3 < 2x
Then, we divide both sides of the inequality by 2 (note: since we are dividing by a positive number, the inequality remains the same):
-3/2 < x
The solution to the inequality -2 < 2x + 1 is x > -3/2.
To solve the inequality -4 < 1, we can immediately see that this statement is true since -4 is indeed less than 1.
Therefore, we can say that both inequalities hold true.
To solve the first inequality, -2 < 2x + 1, we need to isolate the variable x.
Step 1: Start by subtracting 1 from both sides of the inequality:
-2 - 1 < 2x + 1 - 1
-3 < 2x
Step 2: Divide both sides of the inequality by 2:
-3/2 < 2x/2
-3/2 < x
So the solution to the first inequality, -2 < 2x + 1, is x > -3/2.
To solve the second inequality, -4 < 1, we don't need to do anything because it is already in a simplified form.
So the solution to the second inequality, -4 < 1, is true for all values of x.
Overall, we have two inequalities:
1) -2 < 2x + 1, which simplifies to x > -3/2
2) -4 < 1, which is true for all values of x.
Therefore, the solution to these two inequalities is x > -3/2.