Question

which graph shows the solution to the inequality?
$x-(5 - 3x)leq2x - 1$
a. $longleftarrow$ -5 -4 -3 -2 -1 0 1 2 3 4 5 $longrightarrow$
b. $longleftarrow$ -5 -4 -3 -2 -1 0 1 2 3 4 5 $longrightarrow$
c. $longleftarrow$ -5 -4 -3 -2 -1 0 1 2 3 4 5 $longrightarrow$
d. $longleftarrow$ -5 -4 -3 -2 -1 0 1 2 3 4 5 $longrightarrow$

Explanation:

Step1: Simplify the inequality

$x-(5 - 3x)\leq2x - 1$
$x-5 + 3x\leq2x - 1$
$4x-5\leq2x - 1$

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

$4x-2x\leq-1 + 5$
$2x\leq4$

Step3: Solve for $x$

$x\leq2$

Answer:

The graph that has a closed - circle at $2$ and an arrow pointing to the left represents the solution. Without seeing the exact details of the graphs, if the closed - circle is at $2$ and the arrow goes left, that is the correct graph. If we assume the closed - circle indicates the inclusion of the value and the arrow shows the direction of the solution set, the graph with a closed - circle at $2$ and an arrow pointing left is the answer.