1~ a.) Solve a - 9 = 20

b.) Solve b - 9 > 20
c) How is solving the equation in part a similar to solving the inequality in part b?
d.) How are the solutions different?

2~ Briana is allowed to watch no more than 5 hours of T.V a week. So far this week, she has watched 1.5 hours. Write and solve an inequality to show how many hours of T.V Briana can still watch this week.

1. An inequality is treated just like an equation, except that multiplying/dividing by a negative value reverses the carat (< to >).

2. 5 ≥ h - 1.5

1a) To solve the equation a - 9 = 20, we want to isolate the variable 'a' on one side of the equation.

Starting with a - 9 = 20:
Adding 9 to both sides, we get:
a - 9 + 9 = 20 + 9
a = 29

Therefore, the solution to the equation a - 9 = 20 is a = 29.

1b) To solve the inequality b - 9 > 20, we want to isolate the variable 'b' on one side of the inequality.

Starting with b - 9 > 20:
Adding 9 to both sides, we get:
b - 9 + 9 > 20 + 9
b > 29

Therefore, the solution to the inequality b - 9 > 20 is b > 29.

1c) Solving the equation in part a is similar to solving the inequality in part b because both involve isolating the variable on one side of the inequality or equation. However, in the equation, we find an exact solution for 'a' (a = 29), while in the inequality, we find a range of all possible values that satisfy the inequality (b > 29).

1d) The solutions are different in that the equation in part a has an exact value for 'a', while the inequality in part b represents a range of values for 'b'. In the equation, a = 29 is the only solution, while for the inequality, any value of 'b' greater than 29 is a solution.

2) Let's write and solve an inequality to find out how many hours of TV Briana can still watch this week.

Let the number of hours Briana can still watch be represented by 'x'.

Given that she has already watched 1.5 hours, the inequality can be written as:
1.5 + x ≤ 5

To find the value of 'x', we need to isolate it on one side of the inequality.

Starting with 1.5 + x ≤ 5:
Subtracting 1.5 from both sides, we get:
1.5 - 1.5 + x ≤ 5 - 1.5
x ≤ 3.5

Therefore, Briana can still watch up to 3.5 hours of TV this week.

a.) To solve the equation a - 9 = 20, you can isolate the variable by adding 9 to both sides of the equation:

a - 9 + 9 = 20 + 9
a = 29

Therefore, the solution to the equation is a = 29.

b.) To solve the inequality b - 9 > 20, you can isolate the variable by adding 9 to both sides of the inequality:

b - 9 + 9 > 20 + 9
b > 29

Therefore, the solution to the inequality is b > 29.

c.) Solving the equation in part a is similar to solving the inequality in part b because the first step in both cases is to isolate the variable. However, when solving an equation, the goal is to find a specific value that makes the equation true, while when solving an inequality, the goal is to find a range of values that satisfy the inequality.

d.) The solutions to the equation in part a and the inequality in part b are different. In part a, the solution is a single value (a = 29), while in part b, the solution is a range of values (b > 29). This means that any value of b greater than 29 will satisfy the inequality, whereas a specific value of a (a = 29) is the only solution that will make the equation true.

2~ Let x represent the number of hours Briana can still watch TV this week. The inequality to represent this situation is:

1.5 + x ≤ 5

This inequality states that the sum of the hours Briana has already watched (1.5 hours) and the hours she can still watch (x hours) should be less than or equal to the maximum number of hours she can watch, which is 5.

To solve the inequality, subtract 1.5 from both sides of the inequality:

1.5 + x - 1.5 ≤ 5 - 1.5
x ≤ 3.5

Therefore, Briana can still watch a maximum of 3.5 hours of TV this week.