Question

linear inequality and number line (l2)
question
solve the inequality and graph the solution on the line provided.
37 - 6x > -5
answer
attempt 1 out of 2
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
click and drag to plot line.

Explanation:

Step1: Subtract 37 from both sides

To isolate the term with \( x \), we subtract 37 from both sides of the inequality \( 37 - 6x > -5 \). This gives us:

$$ 37 - 37 - 6x > -5 - 37 $$

Simplifying both sides, we get:

$$ -6x > -42 $$

Step2: Divide by -6 (and reverse inequality)

When we divide both sides of an inequality by a negative number, we must reverse the inequality sign. So, we divide both sides of \( -6x > -42 \) by -6:

$$ \frac{-6x}{-6} < \frac{-42}{-6} $$

Simplifying both sides, we find:

$$ x < 7 $$

Answer:

Inequality Notation: \( x < 7 \)