Question

question
solve the inequality and graph the solution on the line provided.
6 + 7x ≤ -15
answer attempt 1 out of 5
< > ≤ ≥ or
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
touch and drag to plot line.
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Explanation:

Step1: Subtract 6 from both sides

To isolate the term with \(x\), we subtract 6 from both sides of the inequality \(6 + 7x\leq - 15\). So we get \(6 + 7x-6\leq - 15 - 6\), which simplifies to \(7x\leq - 21\).

Step2: Divide by 7

Now, we divide both sides of the inequality \(7x\leq - 21\) by 7. Since 7 is a positive number, the direction of the inequality sign remains the same. So \(\frac{7x}{7}\leq\frac{-21}{7}\), which gives \(x\leq - 3\).

Answer:

Inequality Notation: \(x\leq - 3\)
For the number line: We plot a closed circle at \(-3\) (because the inequality is "less than or equal to") and draw an arrow to the left of \(-3\) to represent all numbers less than or equal to \(-3\).