Question

1. graph the solution of the inequality 2x - (3 - x) > x + 1 on the number line.

Explanation:

Step1: Simplify the left - hand side

First, expand $2x-(3 - x)$:
$2x-(3 - x)=2x - 3+x=3x - 3$.
The inequality becomes $3x - 3>x + 1$.

Step2: Move terms with $x$ to one side

Subtract $x$ from both sides:
$3x-x-3>x - x + 1$, which simplifies to $2x-3>1$.

Step3: Isolate the variable term

Add 3 to both sides:
$2x-3 + 3>1 + 3$, so $2x>4$.

Step4: Solve for $x$

Divide both sides by 2:
$\frac{2x}{2}>\frac{4}{2}$, getting $x > 2$.
On a number - line, $x>2$ is represented by an open circle at 2 (since 2 is not included in the solution) and an arrow pointing to the right.

Answer:

The first option (the one with an open circle at 2 and an arrow pointing to the right).