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. b= 29
b. b > 29
a. To solve the equation a - 9 = 20, you need to isolate the variable by performing inverse operations. In this case, you can add 9 to both sides of the equation to cancel out the -9 on the left side:
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 also need to isolate the variable. The process is similar to solving the equation with one key difference. Since the inequality symbol is a greater than sign (>), you need to be careful about the direction of the solution.
To isolate b, you can add 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 and solving the inequality in part b are similar in the sense that you need to isolate the variable on one side of the equation or inequality. Both involve performing inverse operations to cancel out any constants or coefficients attached to the variable.
d. The solutions to the equation and the inequality are different in terms of their interpretation. In part a, the equation a - 9 = 20 has a single solution, which is a = 29. This means that a can only have the value of 29 for the equation to be true.
In part b, the inequality b - 9 > 20 represents a range of possible solutions. The inequality b > 29 indicates that b can take any value greater than 29 for the inequality to hold true. This implies that there are infinitely many solutions for the inequality.