Question

lesson 5-2 example 2 and 3
solve the inequality & graph the solution set.
a) (-\frac{x}{2} - 17 < 7)
the solution set is {x| }
graph the solution

lesson 5-2 example 2 and 3 check
solve the inequality & graph the solution set.
a) (\frac{2x - 4}{6} < -5x + 2)
the solution set is {x| }
graph the solution

(other parts with inequalities like (3 - 4x geq -9 - 2x), (-4x + \frac{3}{4}(4x - 12) geq 3), (3x + 2 geq \frac{1}{2}(x + 5)) etc. from the image are also included but the main focused ones here are the above two for clarity)

Explanation:

Let's solve the inequality \( 3 - 4x \geq -9 - 2x \) step by step.

Step 1: Add \( 4x \) to both sides

To get all the \( x \)-terms on one side, we add \( 4x \) to both sides of the inequality. This gives us:
\( 3 - 4x + 4x \geq -9 - 2x + 4x \)
Simplifying both sides, we have:
\( 3 \geq -9 + 2x \)

Step 2: Add 9 to both sides

Next, we add 9 to both sides to isolate the term with \( x \). So:
\( 3 + 9 \geq -9 + 9 + 2x \)
Simplifying, we get:
\( 12 \geq 2x \)

Step 3: Divide both sides by 2

To solve for \( x \), we divide both sides by 2. Remember that dividing by a positive number doesn't change the direction of the inequality sign.
\( \frac{12}{2} \geq \frac{2x}{2} \)
Simplifying, we find:
\( 6 \geq x \)
Which can also be written as \( x \leq 6 \)

Answer:

The solution set is \( \{ x | x \leq 6 \} \)

For the graphical representation:

• Draw a number line.
• Place a closed circle (since the inequality is "less than or equal to") at 6.
• Shade the line to the left of 6 to represent all numbers less than or equal to 6.