Question

Which graph shows the solution to the inequality? x − (5 − 3x) ≤ 2x − 1 A. A number line with a closed dot at 2 shaded to the left. B. A number line with a closed dot at 2 shaded to the right. C. A number line with a closed dot at negative 1 shaded to the left. D. A number line with a closed dot at negative 1 shaded to the right.

Answer 1

Answer: To solve the inequality x − (5 − 3x) ≤ 2x − 1, we need to simplify it by first distributing the negative sign in front of the parentheses, and then combining like terms. This gives us:

x - 5 + 3x ≤ 2x - 1

4x - 5 ≤ 2x - 1

Next, we can isolate the variable on one side of the inequality by subtracting 2x from both sides:

4x - 2x - 5 ≤ -1

2x - 5 ≤ -1

Finally, we can isolate x by adding 5 to both sides and dividing by 2:

2x ≤ 4

x ≤ 2

So the solution to the inequality is x ≤ 2.

To graph this solution on a number line, we can put a closed dot at 2 and shade to the left of it, since all values less than or equal to 2 satisfy the inequality. Therefore, the correct graph is A, a number line with a closed dot at 2 shaded to the left.

Explanation: