Question

an inequality is shown. 4(x + 2) > 5x - 3 solve the inequality and graph the solution on the number line.

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(4(x + 2)\) to get \(4x+8\). So the inequality becomes \(4x + 8>5x-3\).

Step2: Subtract \(4x\) from both sides

Subtract \(4x\) from each side of the inequality: \(4x+8 - 4x>5x - 3-4x\), which simplifies to \(8>x - 3\).

Step3: Add 3 to both sides

Add 3 to both sides of the inequality: \(8 + 3>x-3 + 3\), which simplifies to \(11>x\) or \(x < 11\).

To graph the solution on the number line: We draw an open circle at \(x = 11\) (since the inequality is strict, \(x
eq11\)) and shade the region to the left of \(11\) to represent all values of \(x\) less than \(11\).

Answer:

The solution to the inequality \(4(x + 2)>5x - 3\) is \(x < 11\). The graph has an open circle at \(11\) and a line (or arrow) extending to the left from \(11\) on the number line.