Part A:
To solve the equation ax - 5 = 18, we need to isolate the variable x. Let's go through the steps:
1. Add 5 to both sides of the equation:
ax - 5 + 5 = 18 + 5
ax = 23
2. Divide both sides of the equation by a:
(ax)/a = 23/a
x = 23/a
So, the solution to the equation is x = 23/a.
Part B:
To solve the inequality ax - 5 > 18, we need to isolate the variable x. Let's go through the steps:
1. Add 5 to both sides of the inequality:
ax - 5 + 5 > 18 + 5
ax > 23
2. Divide both sides of the inequality by a. We need to be cautious here since we don't know the value of a. If a is positive, we can divide by a, and if a is negative, we need to flip the inequality sign:
Case 1: a > 0
(ax)/a > 23/a
x > 23/a
Case 2: a < 0
(ax)/a < 23/a (we flip the inequality sign since we divided by a negative number)
x < 23/a
Therefore, the solution to the inequality ax - 5 > 18 is either x > 23/a (when a > 0) or x < 23/a (when a < 0).
Answer to Questions:
1. The number line set up that would show all of the solutions for the inequality in Part B would have an open circle at 23/a (when a > 0) and an open circle at 23/a (when a < 0), with an arrow extending to the right (when a > 0) or to the left (when a < 0).
2. The difference between solving an equation and an inequality is that when solving an equation, we are looking for a specific value or values that make the equation true, while when solving an inequality, we are looking for a range of values that satisfy the inequality. In an equation, we often have an equal sign, and in an inequality, we have inequality signs such as >, <, ≥, or ≤.
Solve the equation and inequality for x.
Part A: Solve the equation showing all steps.
ax−5=18
Part B: Solve the inequality showing all steps.
ax−5>18
Answer these Questions:
1. Describe the number line set up that would show all of the solutions for the inequality in Part B.
2. State the difference between solving an equation and an inequality
1 answer
1 answer