Part A: To solve the equation ax−5=18, we need to isolate the variable x.
First, we add 5 to both sides of the equation to get:
ax = 18 + 5
ax = 23
Then, we divide both sides of the equation by a to solve for x:
x = 23/a
Therefore, the solution for the equation ax−5=18 is x = 23/a.
Part B: To solve the inequality ax−5>18, we follow similar steps as Part A but with the addition of considering the sign change when multiplying or dividing by a negative number.
First, we add 5 to both sides of the inequality to get:
ax > 18 + 5
ax > 23
Then, we divide both sides of the inequality by a, while considering the sign change:
If a > 0:
x > 23/a
If a < 0:
x < 23/a
Therefore, the solution for the inequality ax−5>18 will be either x > 23/a or x < 23/a, depending on the sign of a.
Part C: The difference between an equation and an inequality regarding solving steps and solutions lies in the nature of the mathematical statement.
An equation is a statement of equality, where the goal is to find the value(s) of the variable(s) that make both sides of the equation equal. The solving steps involve performing operations on both sides of the equation to isolate the variable.
An inequality, on the other hand, is a statement of inequality or comparison between two quantities. The goal is to find the range of values that satisfy the inequality. The solving steps involve similar operations as in solving equations, with the addition of considering the sign change when multiplying or dividing by a negative number. The solutions for an inequality can usually be expressed as a range of values that satisfy the inequality.
16. 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.
1 answer