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?
a=29
b>29
the calculations are the same
(a) is a point
(b) is a region of the number line
a.) To solve the equation a - 9 = 20, we want to isolate the variable "a" on one side of the equation.
Here's how you can do it step-by-step:
Step 1: Add 9 to both sides of the equation to get rid of the -9 on the left side:
a - 9 + 9 = 20 + 9
This simplifies to:
a = 29
So the solution to the equation a - 9 = 20 is a = 29.
b.) To solve the inequality b - 9 > 20, we again want to isolate the variable "b" on one side of the inequality.
Here's how you can do it step-by-step:
Step 1: Add 9 to both sides of the inequality to get rid of the -9 on the left side:
b - 9 + 9 > 20 + 9
This simplifies to:
b > 29
So the solution to the inequality b - 9 > 20 is b > 29.
c.) Solving the equation a - 9 = 20 and solving the inequality b - 9 > 20 both involve the same initial step, which is to add 9 to both sides of the expression.
This step is common because we want to move the constant term (-9) to the opposite side of the equation or inequality.
d.) The solutions to the equation and the inequality are different because solving an equation yields only one unique solution, while solving an inequality can yield multiple solutions.
In the equation a - 9 = 20, the solution is a = 29. This is because when we isolate the variable "a", we find a unique value that satisfies the equation.
On the other hand, in the inequality b - 9 > 20, the solution is b > 29. This means that any value of "b" that is greater than 29 will satisfy the inequality. There are infinitely many possible values for "b" that make the inequality true.