Question

directions
select up to 2 number line button(s) below. click to activate and drag the circles on the number line to graph the answer.
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solve the following inequality and graph the solution set on the number line provided.
15 - 5x < -2(x - 3)

Explanation:

Step1: Expand the right side

First, we expand \(-2(x - 3)\) using the distributive property \(a(b - c)=ab - ac\). So, \(-2(x - 3)=-2x+6\). The inequality becomes \(15 - 5x<-2x + 6\).

Step2: Add \(5x\) to both sides

To get all the \(x\) terms on one side, we add \(5x\) to both sides of the inequality. This gives \(15-5x + 5x<-2x+6 + 5x\), which simplifies to \(15<3x + 6\).

Step3: Subtract 6 from both sides

Next, we subtract 6 from both sides to isolate the term with \(x\). So, \(15 - 6<3x+6 - 6\), which simplifies to \(9<3x\).

Step4: Divide by 3

Finally, we divide both sides by 3 to solve for \(x\). \(\frac{9}{3}<\frac{3x}{3}\), which gives \(3 < x\) or \(x>3\).

To graph this on the number line, we use an open circle at \(x = 3\) (since the inequality is strict, \(x\) is not equal to 3) and draw an arrow to the right to represent all numbers greater than 3.

Answer:

The solution to the inequality \(15 - 5x<-2(x - 3)\) is \(x>3\). On the number line, we place an open circle at \(3\) and shade to the right.