Question

solve for ( x ) and graph the solution on the number line below.
( 0 < 7x )

answer attempt 1 out of 2

( < ) ( > ) ( leq ) ( geq ) or

inequality notation: (\boxed{quad})

number line:
number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12 and arrowheads, with click and drag to plot line text

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Explanation:

Step1: Divide both sides by 7

To solve the inequality \(0 < 7x\), we divide both sides by 7 (since 7 is positive, the inequality sign remains the same). So we have \(\frac{0}{7} < \frac{7x}{7}\).

Step2: Simplify the expressions

Simplifying \(\frac{0}{7}\) gives 0, and simplifying \(\frac{7x}{7}\) gives \(x\). So the inequality becomes \(0 < x\), or equivalently \(x > 0\).

Answer:

Inequality Notation: \(x > 0\)

For the number line: We draw an open circle at 0 (because \(x\) is not equal to 0) and shade the region to the right of 0 to represent all values of \(x\) greater than 0.