11. Solve the in equality: (3mks)
2x – 1 ≤ 3x + 4 < 7 – x
To solve the inequality 2x - 1 ≤ 3x + 4 < 7 - x, we will break it down into two separate inequalities:
1) 2x - 1 ≤ 3x + 4
Rearranging the terms, we get:
-x ≤ 5
Multiplying both sides by -1 (and flipping the inequality sign), we get:
x ≥ -5
2) 3x + 4 < 7 - x
Rearranging the terms, we get:
4x < 3
Dividing both sides by 4, we get:
x < 3/4
Combining the two inequalities, we find:
-5 ≤ x < 3/4
To solve the inequality 2x - 1 ≤ 3x + 4 < 7 - x, we need to break it down into two separate inequalities.
First, let's solve the inequality on the left side:
2x - 1 ≤ 3x + 4
Subtract 2x from both sides:
-1 ≤ x + 4
Subtract 4 from both sides:
-5 ≤ x
So the first inequality is -5 ≤ x.
Next, let's solve the inequality on the right side:
3x + 4 < 7 - x
Add x to both sides:
4x + 4 < 7
Subtract 4 from both sides:
4x < 3
Divide both sides by 4:
x < 3/4
So the second inequality is x < 3/4.
Now we have two separate inequalities:
-5 ≤ x and x < 3/4
To find the solution that satisfies both inequalities, we take the intersection of their solution sets. In other words, we find the values of x that satisfy both -5 ≤ x and x < 3/4.
Since -5 ≤ x, any value of x greater than or equal to -5 satisfies this inequality.
Since x < 3/4, any value of x less than 3/4 satisfies this inequality.
Therefore, the solution is:
-5 ≤ x < 3/4.