Respuesta :
2x − 3 < x + 2
∴ x − 3 < 2
∴ x < 5
x + 2 ≤ 3x + 5
∴ 2 ≤ 2x + 5
∴ -3 ≤ 2x
∴ -3/2 ≤ x
-3/2 ≤ x < 5
∴ x − 3 < 2
∴ x < 5
x + 2 ≤ 3x + 5
∴ 2 ≤ 2x + 5
∴ -3 ≤ 2x
∴ -3/2 ≤ x
-3/2 ≤ x < 5
Answer:
-3/2 ≤ x < 5
Step-by-step explanation:
2x - 3 < x + 2 ≤ 3x+5
Solve the inequality separately
2x-3 <x+2 and x+2≤ 3x+5
LEts solve one by one
2x-3 <x+2
Subtract x from both sides
x -3 < 2
add 3 on both sides
x< 5
x+2≤ 3x+5
Subtract 3x from both sides
-2x + 2 ≤ 5
Subtract 2 from both sides
-2x ≤ 3
Divide both sides by -2
x ≥ -3/2
we got x>= -3/2 and x<5
so x lies between -3/2 and 5
-3/2 ≤ x < 5
