Question

Solve the inequality for x and identify the graph of its solution. 2[x + 3] < 4.

a) x<−1
b) −7c) x>1
d) −1

Answer 1

The inequality 2[x + 3] < 4 is solved by subtracting 3 from 2 and dividing by 2, resulting in x < -1. Option (a) x < -1 is the correct answer, and the graph would be a number line with an open circle on -1 and shading to the left side.

Step-by-step explanation:

To solve the inequality 2[x + 3] < 4, we begin by removing the brackets and dividing both sides of the inequality by 2:

• 2(x + 3) < 4
• x + 3 < 2
• x < 2 - 3
• x < -1

In this case, the solution to the inequality is x < -1. The graph of its solution is a number line with an open circle at -1 and shading to the left, as numbers to the left of -1 fulfill the condition x < -1.

Regarding options provided by the student:

1. x < -1 (correct answer)
2. −7
3. x > 1
4. −1

The correct answer, in this case, is option (a): x < -1.