Question

solve and graph the following inequality: 3x - 2 ≥ -14 provide an answer accurate to the nearest tenth. inequality: text box graph: number line options button, trash can icon, number line with a marker and four arrow options (open/closed circles, left/right)

Explanation:

Step1: Add 2 to both sides

To isolate the term with \( x \), we add 2 to both sides of the inequality \( 3x - 2 \geq -14 \). This gives us \( 3x - 2 + 2 \geq -14 + 2 \), which simplifies to \( 3x \geq -12 \).

Step2: Divide by 3

Next, we divide both sides of the inequality \( 3x \geq -12 \) by 3 to solve for \( x \). So, \( \frac{3x}{3} \geq \frac{-12}{3} \), which simplifies to \( x \geq -4.0 \) (since we need to be accurate to the nearest tenth).

For the graph: Since the inequality is \( x \geq -4.0 \), we use a closed circle at \( -4.0 \) on the number line (because the inequality includes equality, \( \geq \)) and shade to the right of \( -4.0 \) to represent all values of \( x \) that satisfy the inequality.

Answer:

Inequality: \( x \geq -4.0 \)
Graph: A closed circle at \( -4.0 \) on the number line with shading to the right. (Using the number line options, select the "closed circle (•) pointing to the right (→)" option, placing the closed circle at \( -4.0 \))