Question

solve and graph
a. solve $25 - 4x < 1$.
b. graph the solutions to the inequality.

Explanation:

Part a: Solve \( 25 - 4x < 1 \)

Step 1: Subtract 25 from both sides

To isolate the term with \( x \), we subtract 25 from both sides of the inequality.
\( 25 - 4x - 25 < 1 - 25 \)
Simplifying both sides gives:
\( -4x < -24 \)

Step 2: Divide by -4 (and reverse inequality)

When dividing an inequality by a negative number, we reverse the inequality sign. We divide both sides by -4.
\( \frac{-4x}{-4} > \frac{-24}{-4} \)
Simplifying both sides gives:
\( x > 6 \)

Answer:

\( x > 6 \)

Part b: Graph the solution \( x > 6 \)

To graph \( x > 6 \) on a number line:

1. Locate 6 on the number line.
2. Draw an open circle at 6 (since \( x \) is not equal to 6, only greater than).
3. Draw an arrow to the right of 6 to indicate all numbers greater than 6 are part of the solution.

(Note: The given number line in the image has markings at -9, -6, -3, 0, 3, 6, 9. To graph \( x > 6 \), place an open circle at 6 and draw an arrow pointing to the right (towards 9 and beyond).)