Which numbers are in the solution set of the inequality 1.4(d–2)–0.2d≤3.2? Select all that apply.

Question

-2
7
35/5
5
-3
0

Answer 1

To solve the inequality \( 1.4(d - 2) - 0.2d \leq 3.2 \), we first simplify the expression:

1. Distribute \( 1.4 \) in the left-hand side: \[ 1.4d - 2.8 - 0.2d \leq 3.2 \]

2. Combine like terms: \[ (1.4d - 0.2d) - 2.8 \leq 3.2 \] \[ 1.2d - 2.8 \leq 3.2 \]

3. Add \( 2.8 \) to both sides: \[ 1.2d \leq 3.2 + 2.8 \] \[ 1.2d \leq 6 \]

4. Divide both sides by \( 1.2 \): \[ d \leq \frac{6}{1.2} \] Simplifying \( \frac{6}{1.2} \): \[ d \leq 5 \]

Now we need to find the numbers from the options that are less than or equal to \( 5 \).

Let's check each option:

• \(-2\): Less than \( 5 \) (included)
• \(7\): Greater than \( 5 \) (not included)
• \(\frac{35}{5} = 7\): Greater than \( 5 \) (not included)
• \(5\): Equal to \( 5 \) (included)
• \(-3\): Less than \( 5 \) (included)
• \(0\): Less than \( 5 \) (included)

Thus, the numbers that are in the solution set of the inequality are:

• \(-2\)
• \(5\)
• \(-3\)
• \(0\)

The final answers are \(-2\), \(5\), \(-3\), and \(0\).