1-Variable Equations & Inequalities Discussion

Question

1-Variable Equations & Inequalities Discussion

Think about the differences between equations and inequalities. For what purpose do you use each one? How is solving for them the same and how is it different?

Create and share a real-world scenario for which you will create an inequality and equation that requires at least two steps to solve. After you have created and shared your own scenario, solve the scenarios shared by two of your peers.

In your response to each post:

Write the solution to both the inequality and the equation.
Explain how the inequality and the equation work together in the scenario.
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in 3 to 5 sentances

Answer 1

Bot GPT 4-o mini answered
2 hours ago

Equations are used when we want to find a specific value that satisfies a relationship, while inequalities help us understand a range of possible values. Solving an equation gives us an exact answer, while solving an inequality provides a set of solutions within certain limits. Both involve similar algebraic techniques, such as isolating the variable, but inequalities require an understanding of greater than or less than relationships.

Here's a real-world scenario: A company pays its employees a base salary of $40,000 per year plus a commission of $500 for each sale made. An employee wants to determine how many sales they need to make to earn at least $60,000 in a year (inequality) and what their total earnings would be if they made 30 sales (equation).

Inequality: $ 40,000 + 500s \geq 60,000 $ Equation: $ 40,000 + 500(30) = T $

In solving the inequality:

Subtract 40,000 from both sides: $ 500s \geq 20,000 $
Divide by 500: $ s \geq 40 $

In solving the equation:

$ T = 40,000 + 500(30) $
$ T = 40,000 + 15,000 = 55,000 $

The inequality indicates that the employee needs to make at least 40 sales to reach their income goal, while the equation shows that making 30 sales would result in earnings of $55,000, which is below the target. This demonstrates how the equation confirms the earnings from a specific number of sales, while the inequality sets a minimum requirement to achieve a desired financial outcome.