Questions: Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line. 4(3-5x)<28-4x Select the correct answer below and, if necessary, fill in the answer box to complete your choice. A. The solution set expressed in interval notation is (Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The solution set is ∅. Choose the correct graph of the inequality below. A. B. C. D.

Solution Steps

To solve the inequality \(4(3 - 5x) < 28 - 4x\), we need to follow these steps:

1. Distribute the 4 on the left side of the inequality.
2. Combine like terms.
3. Isolate the variable \(x\) on one side of the inequality.
4. Solve for \(x\).
5. Express the solution in interval notation.
6. Graph the solution set on a number line.

1. Distribute the 4 on the left side: \(4 \cdot 3 - 4 \cdot 5x < 28 - 4x\).
2. Simplify the expression: \(12 - 20x < 28 - 4x\).
3. Move all terms involving \(x\) to one side and constants to the other: \(12 - 28 < 20x - 4x\).
4. Simplify and solve for \(x\): \(-16 < 16x\), which gives \(x > -1\).
5. Express the solution in interval notation: \((-1, \infty)\).
6. Graph the solution set on a number line.

Given the inequality: \[ 4(3 - 5x) < 28 - 4x \]

First, distribute the 4 on the left-hand side: \[ 4 \cdot 3 - 4 \cdot 5x < 28 - 4x \] \[ 12 - 20x < 28 - 4x \]

Next, we need to get all the \( x \)-terms on one side and the constants on the other side. Add \( 20x \) to both sides: \[ 12 - 20x + 20x < 28 - 4x + 20x \] \[ 12 < 28 + 16x \]

Subtract 28 from both sides: \[ 12 - 28 < 16x \] \[ -16 < 16x \]

Divide both sides by 16: \[ \frac{-16}{16} < x \] \[ -1 < x \]

The solution in interval notation is: \[ (-1, \infty) \]

To graph the solution set on a number line, we draw an open circle at \( x = -1 \) and shade the line to the right of \( -1 \).

Final Answer