Question

For each inequality, decide whether the solutions is represented by x < 2.5 or x >2.5

1. -4x + 5 > -5. 2. -25 > -5(x + 2.5)

Answer 1

#1

• -4x+5>-5
• -4x>-5-5
• -4x>-10
• 4x<10
• x<2.5

#2

• -25>-5(x+2.5)
• 25<5(x+2.5)
• x+2.5>5
• x>2.5

Answer 2

1. x < 2.5

2. x > 2.5

Explanation:

Question 1

Given inequality:

-4x + 5 > -5

Subtract 5 from both sides:

⇒ -4x + 5 - 5 > -5 - 5

⇒ -4x > -10

Divide both sides by -4 (remembering to flip the sign as we are dividing by a negative):

⇒ -4x ÷ -4 > -10 ÷ -4

⇒ x < 2.5

Question 2

Given inequality:

-25 > -5(x + 2.5)

Expand the brackets:

⇒ -25 > -5x - 12.5

Add 12.5 to both sides:

⇒ -25 + 12.5 > -5x - 12.5 + 12.5

⇒ -12.5 > -5x

Divide both sides by -5 (remembering to flip the sign as we are dividing by a negative):

⇒ -12.5 ÷ -5 > -5x ÷ -5

⇒ 2.5 < x

⇒ x > 2.5