Question

solve the inequality. graph the solution.
|6x - 3|+3 < 45
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question 3 of 9

Explanation:

Step1: Isolate the absolute - value expression

Subtract 3 from both sides of the inequality \(|6y - 3|+3\lt45\). We get \(|6y - 3|\lt42\).

Step2: Apply the absolute - value property

If \(|a|\lt b\) (\(b\gt0\)), then \(-b\lt a\lt b\). So, \(- 42\lt6y - 3\lt42\).

Step3: Solve the compound inequality

Add 3 to all parts: \(-42 + 3\lt6y-3 + 3\lt42 + 3\), which simplifies to \(-39\lt6y\lt45\).

Step4: Divide by 6

Divide each part of the inequality \(-39\lt6y\lt45\) by 6. We have \(\frac{-39}{6}\lt y\lt\frac{45}{6}\), or \(-\frac{13}{2}\lt y\lt\frac{15}{2}\), which is \(-6.5\lt y\lt7.5\).
The solution on the number - line is a line segment between \(-6.5\) and \(7.5\) with open circles at the endpoints.

Answer:

The graph that shows an open - ended line segment between approximately \(-6.5\) and \(7.5\) (open circles at the endpoints) is the correct one. Without seeing the exact details of the graphs in terms of scale and precision, if we assume the number - line is marked in whole numbers, the graph should have an open circle at \(y=-6\) and an open circle at \(y = 7\) and a line connecting them.