Question

solve the inequality and graph the solution on the line provided.
-6 + 7x > 1
answer attempt 1 out of 2
< > ≤ ≥ or
inequality notation:
number line:

Explanation:

Step1: Isolate the term with \(x\)

Add \(6\) to both sides of the inequality \(-6 + 7x>1\).
Using the addition property of inequalities (\(a>b\) implies \(a + c>b + c\)), we get \(-6+7x + 6>1 + 6\), which simplifies to \(7x>7\).

Step2: Solve for \(x\)

Divide both sides of the inequality \(7x>7\) by \(7\).
Using the division property of inequalities (\(a>b\) and \(c>0\) implies \(\frac{a}{c}>\frac{b}{c}\)), we have \(\frac{7x}{7}>\frac{7}{7}\), so \(x > 1\).

Answer:

Inequality Notation: \(x>1\)

To graph \(x > 1\) on the number - line:

1. Draw an open circle at \(x = 1\) (because \(x = 1\) is not included in the solution set, since the inequality is \(>\)).
2. Draw an arrow to the right of \(x = 1\) to represent all values of \(x\) greater than \(1\).