Question

Solve the equation and inequality for x.

Part A: Solve the equation for x showing all steps for credit: ax − 5 = 18
Part B: Solve the inequality for x showing all steps for credit: ax − 5 > 18
Part C: State the difference between an equation and an inequality regarding solving steps and solutions.

Answer 1

Part A:
To solve the equation ax - 5 = 18, we need to isolate the variable x by undoing the operations in reverse order.

First, we can add 5 to both sides of the equation:
ax - 5 + 5 = 18 + 5
ax = 23

Next, we divide both sides by a to solve for x:
(ax) / a = 23 / a
x = 23 / a

Therefore, the solution for x is x = 23 / a.

Part B:
To solve the inequality ax - 5 > 18, we again need to isolate the variable x.

First, we can add 5 to both sides of the equation:
ax - 5 + 5 > 18 + 5
ax > 23

Next, we divide both sides by a to solve for x:
(ax) / a > 23 / a
x > 23 / a

Therefore, the solution for the inequality is x > 23 / a.

Part C:
The difference between an equation and an inequality lies in the solutions.

An equation has a single value or set of values that make both sides of the equation equal. Once the equation is solved, the solution(s) will give a specific numerical value or values for the variable.

An inequality, on the other hand, represents a range of values that satisfy the inequality. Once the inequality is solved, the solution(s) will give a range of values or an interval for the variable that makes the inequality true.

Therefore, when solving an equation, we find specific values for the variable, while when solving an inequality, we find a range of values for the variable that satisfies the inequality.