Question

Solve for x: 7x + 39 ≥ 53 and 16x + 15 > 31 A) x > 1 B) x ≥ 2 C) x ≤ 2 D) There are no solutions E) All values of x are solutions

Answer 1

To solve the given set of inequalities, first isolate x in each inequality, then find their intersection.

Step-by-step explanation:

To solve the inequality 7x + 39 ≥ 53, we need to isolate x. First, subtract 39 from both sides: 7x ≥ 14. Then divide both sides by 7: x ≥ 2. So the solution to this inequality is x ≥ 2.

Now let's solve the inequality 16x + 15 > 31. Start by subtracting 15 from both sides: 16x > 16. Next, divide both sides by 16: x > 1. So the solution to this inequality is x > 1.

Since we have two inequalities, we need to find the intersection of their solutions. In this case, the intersection is x > 1, because 1 is the largest value that satisfies both inequalities.

Answer 2

The accurate response is A) x > 1.

Let's address each inequality individually:

1. 7x + 39 ≥ 53

By subtracting 39 from both sides, we obtain:

7x ≥ 14

Dividing both sides by 7 (while reversing the inequality sign due to dividing by a negative number):

x ≥ 2

2. 16x + 15 > 31

Deducting 15 from both sides:

Upon dividing both sides by 16:

x > 1

Now, let's examine both inequalities simultaneously. We seek the values of x that meet both conditions, necessitating the intersection of the solution sets:

`x \geq 2 \cap x > 1`

This simplifies to x > 1.

Question:

Solve for x: 7x + 39 ≥ 53 and 16x + 15 > 31

A) x > 1

B) x ≥ 2

C) x ≤ 2

D) There are no solutions

E) All values of x are solutions