Part A: Solve the equation for x showing all steps for credit: ax - 5 = 18
Step 1: Add 5 to both sides of the equation:
ax - 5 + 5 = 18 + 5
ax = 23
Step 2: Divide both sides of the equation by a:
ax/a = 23/a
x = 23/a
Therefore, the solution to the equation ax - 5 = 18 is x = 23/a.
Part B: Solve the inequality for x showing all steps for credit: ax - 5 > 18
Step 1: Add 5 to both sides of the inequality:
ax - 5 + 5 > 18 + 5
ax > 23
Step 2: Divide both sides of the inequality by a. However, if a is negative, the direction of the inequality sign must be reversed:
If a > 0:
ax/a > 23/a
x > 23/a
If a < 0:
ax/a < 23/a
x < 23/a
Therefore, the solution to the inequality ax - 5 > 18 is either x > 23/a (if a > 0) or x < 23/a (if a < 0).
Part C: The main difference between an equation and an inequality regarding solving steps and solutions is the range of possible solutions.
In an equation, we are looking for a specific value or set of values that satisfy the equation. We can solve it by performing operations on both sides to isolate the variable.
In an inequality, we are looking for a range of values that satisfy the inequality. We can solve it by performing operations on both sides, but we need to consider the direction of the inequality sign and whether the variable may be positive or negative.
Equations have exact solutions, while inequalities have solution sets representing a range or interval of values.
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.
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