Question

linear inequality and number line (l2)
question
solve the inequality and graph the solution on the line provided.
$57 + 6x \geq 45$
answer
attempt 1 out of 2
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
click and drag to plot line.

Explanation:

Step1: Subtract 57 from both sides

To isolate the term with \( x \), we subtract 57 from both sides of the inequality \( 57 + 6x \geq 45 \). This gives us \( 6x \geq 45 - 57 \). Calculating the right - hand side, \( 45-57=-12 \), so the inequality becomes \( 6x \geq - 12 \).

Step2: Divide both sides by 6

Now, to solve for \( x \), we divide both sides of the inequality \( 6x \geq - 12 \) by 6. Since 6 is a positive number, the direction of the inequality sign remains the same. So, \( x\geq\frac{-12}{6} \), and \( \frac{-12}{6}=-2 \). So the solution to the inequality is \( x\geq - 2 \).

Answer:

Inequality Notation: \( x\geq - 2 \)
For the number line: We would plot a closed circle at \( x = - 2 \) (because the inequality is "greater than or equal to") and draw an arrow to the right (since \( x \) is greater than or equal to - 2) starting from - 2.