Question

directions: answer each of the following questions. show all work.

1. graph: -3 < x
2. using your graph from #1, list 3 possible solutions.
3. solve and graph: 8 - 3x ≤ 26
4. solve and graph: 2(2x + 1) ≤ 178
5. write the inequality symbol for each phrase below:

≥
<
≤

1. given the following inequalities, identify the circle type & direction of shading.

≥
<
≤

1. solve the following and state three solutions: -7x + 1 < 36
2. an elevator picks you up on the fifth floor. you ascend three floors, descend six floors, then stop. what floor are you on now?

Explanation:

Step1: Solve the inequality \(8 - 3x\leq26\)

Subtract \(8\) from both sides:
\(8-3x - 8\leq26 - 8\)
\(-3x\leq18\)
Divide both sides by \(-3\) and reverse the inequality sign (since dividing by a negative number):
\(x\geq - 6\)

Step2: Graph \(x\geq - 6\)

On the number - line, put a closed circle at \(-6\) (because the inequality is \(\geq\)) and shade to the right.

Step3: Solve the inequality \(2(2x + 1)\leq178\)

First, distribute the \(2\):
\(4x+2\leq178\)
Subtract \(2\) from both sides:
\(4x+2 - 2\leq178 - 2\)
\(4x\leq176\)
Divide both sides by \(4\):
\(x\leq44\)

Step4: Graph \(x\leq44\)

On the number - line, put a closed circle at \(44\) (because the inequality is \(\leq\)) and shade to the left.

Step5: Solve the inequality \(-7x + 1\lt36\)

Subtract \(1\) from both sides:
\(-7x+1 - 1\lt36 - 1\)
\(-7x\lt35\)
Divide both sides by \(-7\) and reverse the inequality sign:
\(x\gt - 5\)
Three possible solutions (any numbers greater than \(-5\)): \(x = 0\), \(x = 1\), \(x = 2\)

Step6: Solve the elevator problem

Start on the \(5^{th}\) floor. Ascend \(3\) floors: \(5 + 3=8\)
Descend \(6\) floors: \(8-6 = 2\)

Answer:

1. Graph: Open circle at \(-3\) and shade to the right.
2. Possible solutions (e.g.): \(x=-2\), \(x = 0\), \(x = 1\)
3. Solution: \(x\geq - 6\); Graph: Closed circle at \(-6\), shade right.
4. Solution: \(x\leq44\); Graph: Closed circle at \(44\), shade left.
5. \(>\): greater than; \(\geq\): greater than or equal to; \(<\): less than; \(\leq\): less than or equal to
6. \(>\): Open circle, shade right; \(\geq\): Closed circle, shade right; \(<\): Open circle, shade left; \(\leq\): Closed circle, shade left
7. Solution: \(x\gt - 5\); Solutions: \(0\), \(1\), \(2\)
8. \(2^{nd}\) floor