Question

Is 4 the solution to the equation and the boundary point for the inequality? (1) j - 4 ≤ -8, (2) j - 4 = -8, (3) j = -4. (A) Yes (B) No

Answer 1

No, 4 is not the solution to the equation and the boundary point for the inequality.

Step-by-step explanation:

In order to determine if 4 is the solution to the equation and the boundary point for the inequality, we will substitute the value of 4 into each expression and check if the equation or inequality is true.

(1) j - 4 ≤ -8: Substitute 4 for j --> 4 - 4 ≤ -8 --> 0 ≤ -8, which is false. Therefore, 4 is not a solution to the inequality.

(2) j - 4 = -8: Substitute 4 for j --> 4 - 4 = -8 --> 0 = -8, which is false. Therefore, 4 is not a solution to the equation.

(3) j = -4: Substitute 4 for j --> 4 = -4, which is false. Therefore, 4 is not a solution to the equation.

Based on our substitutions, we can conclude that 4 is not the solution to the equation and the boundary point for the inequality.

Answer 2

Since the solution to the inequality is j ≤ -4 and the boundary point is -4, the correct answer is (A) Yes.

To determine the solution to the equation and the boundary point for the inequality, let's analyze each statement:

(1) j - 4 ≤ -8:

To find the solution to this inequality, we need to isolate the variable j.

Adding 4 to both sides of the inequality, we get:

j ≤ -8 + 4

j ≤ -4

The solution to the inequality is j ≤ -4.

Since the inequality uses the "less than or equal to" symbol (≤), the boundary point (-4) is included in the solution.

(2) j - 4 = -8:

This is an equation, not an inequality. To solve for j, we can add 4 to both sides of the equation:

j - 4 + 4 = -8 + 4

j = -4

The solution to the equation is j = -4.

(3) j = -4:

This is also an equation. The solution to this equation is j = -4.