Question

1. solve the inequality. graph the solution on a number line and write the final answer as an inequality. please show your work. 3(x - 4) > -2x + 3

Explanation:

Step1: Expand the left side

First, we expand \(3(x - 4)\) using the distributive property \(a(b - c)=ab - ac\). So we get \(3x-12\). The inequality becomes \(3x - 12>-2x + 3\).

Step2: Add \(2x\) to both sides

To get all the \(x\) terms on one side, we add \(2x\) to both sides of the inequality. This gives \(3x+2x - 12>-2x+2x + 3\), which simplifies to \(5x - 12>3\).

Step3: Add 12 to both sides

Next, we add 12 to both sides to isolate the term with \(x\). So \(5x-12 + 12>3 + 12\), which simplifies to \(5x>15\).

Step4: Divide by 5

Finally, we divide both sides by 5 to solve for \(x\). \(\frac{5x}{5}>\frac{15}{5}\), which gives \(x > 3\).

Answer:

The solution to the inequality \(3(x - 4)>-2x + 3\) is \(x>3\). To graph this on a number line, we draw an open circle at \(x = 3\) (since the inequality is strict, \(x
eq3\)) and shade the region to the right of 3, indicating all values of \(x\) greater than 3.