Question

name: yeslin 01-07-26
x > 2
x ≤ 4
4 < x ≤ 2
left)

1. 15 < 2x + 11
2. \\(\frac{2}{5}x - 7 ≤ 3\\)
3. x - 8 ≥ 3x + 14
4. 3x + 25 + 2x - 5 < 10

Explanation:

Let's solve each inequality one by one.

Problem 2: \( 15 < 2x + 11 \)

Step 1: Subtract 11 from both sides

To isolate the term with \( x \), we subtract 11 from both sides of the inequality.
\( 15 - 11 < 2x + 11 - 11 \)
\( 4 < 2x \)

Step 2: Divide both sides by 2

To solve for \( x \), we divide both sides of the inequality by 2.
\( \frac{4}{2} < \frac{2x}{2} \)
\( 2 < x \) or \( x > 2 \)

Step 1: Add 7 to both sides

To isolate the term with \( x \), we add 7 to both sides of the inequality.
\( \frac{2}{5}x - 7 + 7 \leq 3 + 7 \)
\( \frac{2}{5}x \leq 10 \)

Step 2: Multiply both sides by \( \frac{5}{2} \)

To solve for \( x \), we multiply both sides of the inequality by \( \frac{5}{2} \).
\( \frac{5}{2} \times \frac{2}{5}x \leq 10 \times \frac{5}{2} \)
\( x \leq 25 \)

Step 1: Subtract \( x \) from both sides

To get all \( x \) terms on one side, we subtract \( x \) from both sides.
\( x - 8 - x \geq 3x + 14 - x \)
\( -8 \geq 2x + 14 \)

Step 2: Subtract 14 from both sides

To isolate the term with \( x \), we subtract 14 from both sides.
\( -8 - 14 \geq 2x + 14 - 14 \)
\( -22 \geq 2x \)

Step 3: Divide both sides by 2

To solve for \( x \), we divide both sides of the inequality by 2.
\( \frac{-22}{2} \geq \frac{2x}{2} \)
\( -11 \geq x \) or \( x \leq -11 \)

Answer:

\( x > 2 \)

Problem 4: \( \frac{2}{5}x - 7 \leq 3 \)