Question

which number line represents the solution to (2.5 - 1.2x < 6.5 - 3.2x)?

Explanation:

Write down the inequality

We begin with the given inequality:

$$2.5 - 1.2x < 6.5 - 3.2x$$

Solve the linear inequality

Using the Solving Linear Inequalities knowledge point, we isolate the variable \(x\). Add \(3.2x\) to both sides:

$$2.5 + 2x < 6.5$$

Subtract \(2.5\) from both sides:

$$2x < 4$$

Divide by \(2\):

$$x < 2$$

Determine the number line representation

Using the Number Line Representation knowledge point, we represent \(x < 2\) visually:

• An open circle at \(2\) indicates that \(2\) is not included.
• An arrow pointing to the left represents all values less than \(2\).

Match with the given options

Looking at the four options from left to right:

• Option 1: Open circle at \(4\), arrow pointing right.
• Option 2: Open circle at \(2\), arrow pointing right.
• Option 3: Open circle at \(2\), arrow pointing left.
• Option 4: Open circle at \(4\), arrow pointing left.

The third option correctly represents \(x < 2\).

Answer:

• (A) Open circle at 4, arrow pointing right
• (B) Open circle at 2, arrow pointing right
• (C) Open circle at 2, arrow pointing left (Correct answer)
• (D) Open circle at 4, arrow pointing left