Answer:
Explanation:
a) To solve the inequality x + 5 ≥ 7, we follow these steps:
Subtract 5 from both sides of the inequality:
x + 5 - 5 ≥ 7 - 5
Simplifying this we get:
x ≥ 2
We can represent the solution x ≥ 2 on a number line by placing a closed circle at 2 and shading all the values to the right of 2. This is because x can be equal to 2 or any value greater than 2.
Here's a visual representation of the solution on a number line:
----|----|----|----|----|----|----|----|----|----|
-2 0 2 4 6 8 10 12 14 16
◯----⟶
The closed circle represents x = 2, and the shading to the right represents all the values of x that satisfy the inequality x + 5 ≥ 7.
b) To solve the inequality 3x + 5 < 2, we follow these steps:
Subtract 5 from both sides of the inequality:
3x + 5 - 5 < 2 - 5
Simplifying this we get:
3x < -3
Divide both sides of the inequality by 3. Since we are dividing by a negative number, we must flip the inequality sign to maintain the inequality.
(3x)/3 > -3/3
Simplifying this we get:
x < -1
We can represent the solution x < -1 on a number line by placing an open circle at -1 and shading all the values to the left of -1. This is because x cannot be equal to -1, only less than -1.
Here's a visual representation of the solution on a number line:
----|----|----|----|----|----|----|----|----|----|
-2 0 -1 2 4 6 8 10 12 14
⟶----◯
The open circle represents x < -1, and the shading to the left represents all the values of x that satisfy the inequality 3x + 5 < 2.