Math  /  Algebra

QuestionWed Noy 30 15441 mylab, pearson.com llege Algebra - FL 2024 Quanto Griffin nework: HW Units 1.4 \& 1.6 1.4 .27 HW Seores 22.58%,722.58 \%, 7 of 31 peints Part 1 of 2 Points: 0 of 1 Save on list Solve. Then graph. 7x287 x \geq 28 Choose the solution. A. {xx<4}\{x \mid x<4\} B. (xx4)(x \mid x \leqslant 4) C. {xx>4}\{x \mid x>4\} D. (xx=4)(x \mid x=4) Clear all Skill builder Cheek answer

Studdy Solution

STEP 1

What is this asking? We need to find all the numbers xx that, when multiplied by 7, are greater than or equal to 28, and then draw them on a number line! Watch out! Don't forget to flip the inequality sign if you multiply or divide by a negative number, but we're not doing that here, so we're good!

STEP 2

1. Solve the inequality.
2. Graph the solution.

STEP 3

We have 7x287x \geq 28.
We want to get xx all by itself.
Since xx is multiplied by **7**, we'll divide both sides of the inequality by **7**.
Remember, what we do to one side, we *must* do to the other to keep things balanced!

STEP 4

7x7287 \frac{7x}{7} \geq \frac{28}{7} Why are we dividing by 7?
Because we're effectively dividing to one to isolate xx! 77x287 \frac{7}{7} \cdot x \geq \frac{28}{7} 1x4 1 \cdot x \geq 4 x4 x \geq 4 So, xx can be any number greater than or equal to **4**!

STEP 5

Draw a horizontal line representing the number line.
Mark the number **4** on it with a **filled-in circle**, because xx *can* be equal to **4**.

STEP 6

Since our solution is x4x \geq 4, we shade the part of the number line to the *right* of **4**, including **4** itself.
This visually represents all the numbers greater than or equal to **4**.
An arrow at the end of the shaded region shows that it goes on forever in that direction!

STEP 7

The solution to the inequality 7x287x \geq 28 is x4x \geq 4, which corresponds to answer choice D, {xx4}\{x \mid x \geq 4\}.
The graph is a number line with a filled-in circle at **4** and shading to the right.

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