Question

select the graph that represents the solution to: $x-(5 - 3x)leq2x - 1$

Explanation:

Step1: Simplify the left - hand side

First, simplify $x-(5 - 3x)$:
$x-5 + 3x=4x-5$. So the inequality becomes $4x-5\leq2x - 1$.

Step2: Move the terms with $x$ to one side

Subtract $2x$ from both sides:
$4x-2x-5\leq2x-2x - 1$, which simplifies to $2x-5\leq - 1$.

Step3: Isolate the variable term

Add 5 to both sides:
$2x-5 + 5\leq-1 + 5$, resulting in $2x\leq4$.

Step4: Solve for $x$

Divide both sides by 2:
$\frac{2x}{2}\leq\frac{4}{2}$, so $x\leq2$.

Answer:

The graph with a closed - circle at 2 and an arrow pointing to the left (the fourth graph in the order from top - to - bottom as described in the problem) represents the solution set of the inequality $x-(5 - 3x)\leq2x - 1$.