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Eric is solving the inequality 9x + 15 ≥

51 and graphing the solution. Which of the following describe the steps he should take using inverse operations to solve? (1 point)
Responses

Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.
Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.

Divide both sides of the inequality by 9 and then add 15 to both sides of the inequality.
Divide both sides of the inequality by 9 and then add 15 to both sides of the inequality.

Divide both sides of the inequality by 9 and then subtract 15 from both sides of the inequality.
Divide both sides of the inequality by 9 and then subtract 15 from both sides of the inequality.

Subtract 15 from both sides of the inequality and then multiply both sides of the inequality by 9.
Subtract 15 from both sides of the inequality and then multiply both sides of the inequality by 9.
Question 2
Help Eric draw his answer on the number line by selecting the correct responses below.

(2 points)
Eric would plot the point given in the solution on the number line with a(n)
circle and shade to the
of the point on the number line.

1 answer

To solve the inequality \(9x + 15 \geq 51\):

  1. Subtract 15 from both sides of the inequality: \[9x + 15 - 15 \geq 51 - 15\] \[9x \geq 36\]

  2. Divide both sides by 9: \[x \geq 4\]

So, the correct response describing the steps he should take is: Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.

Question 2:

Since the solution to the inequality is \(x \geq 4\), when graphing this on a number line:

  • You would plot the point at \(4\) with a closed circle (because \(x\) can be equal to \(4\)).
  • You would shade to the right of the point on the number line (indicating all values greater than \(4\)).

Thus, the correct response is: Eric would plot the point given in the solution on the number line with a closed circle and shade to the right of the point on the number line.