Question

Solve the inequality- 5/2(3x+4)<6-3x. Show your work.

Answer 1

x < -8/21

Explanation:

Step 1: Simplify both sides of the equation.

• 
  `((5)/(2) * 3x) + ((5)/(2) * 4) < -3x + 6`
• 
  `(15)/(2)x + 10 < -3x + 6`

Step 2: Add 3x to both sides.

• 
  `(15)/(2)x + 10 + 3x < -3x + 6 + 3x`
• 
  `(21)/(2)x + 10 < 6`

Step 3: Subtract 10 from both sides.

• 
  `(21)/(2)x + 10 - 10 < 6 - 10`
• 
  `(21)/(2)x < -4`

Step 4: Multiply both sides by 2/21.

• 
  `(21)/(2)x * (2)/(21) < -4 * (2)/(21)`
  `x < -(8)/(21)`

Therefore, the answer is x < -8/21.