Question

Solve the inequality 2x - 3 < x 2 ≤ 3x 5. show your work

Answer 1

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

Answer 2

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