Question

question
solve the inequality and graph the solution on the line provided.
$-5x + 8 > 3$

answer attempt 1 out of 2

inequality notation:

number line:

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
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Explanation:

Step1: Subtract 8 from both sides

To isolate the term with \( x \), we subtract 8 from both sides of the inequality \( -5x + 8 > 3 \). This gives us \( -5x + 8 - 8 > 3 - 8 \), which simplifies to \( -5x > -5 \).

Step2: Divide by -5 (reverse inequality)

When dividing both sides of an inequality by a negative number, we must reverse the inequality sign. Dividing both sides of \( -5x > -5 \) by -5 gives \( \frac{-5x}{-5} < \frac{-5}{-5} \), which simplifies to \( x < 1 \).

Answer:

Inequality Notation: \( x < 1 \)

For the number line: Draw an open circle at 1 (since \( x \) is not equal to 1) and shade the region to the left of 1 to represent all values of \( x \) less than 1.