Question

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

Explanation:

Step1: Expand the left - hand side

$4(x + 2)=4x+8$, so the inequality becomes $4x + 8>5x - 3$.

Step2: Move the $x$ terms to one side

Subtract $4x$ from both sides: $4x+8-4x>5x - 3-4x$, which simplifies to $8>x - 3$.

Step3: Isolate $x$

Add 3 to both sides: $8 + 3>x-3 + 3$, resulting in $11>x$ or $x<11$.

To graph on the number - line:

1. Draw a number line with numbers from - 14 to 14.
2. Place an open circle at 11 (because the inequality is $x<11$, not $x\leq11$).
3. Shade the line to the left of 11 to represent all the values of $x$ that satisfy the inequality.

Answer:

The solution of the inequality is $x<11$. On the number line, there is an open circle at 11 and the line is shaded to the left of 11.