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Linear Inequalities

When is 2x greater than x? Compare algebraic expressions with linear inequalities.

Word Problems

         

Consider two successive even numbers. If 10 is subtracted from 4 times the smaller one, then the resulting value is smaller than 2 times the larger one. What is the maximum possible value of the sum of the two successive even numbers?

Adam took an exam with \(20\) questions, and answered all of the \(20\) questions. He gets \(5\) points for a right answer and \(2\) points taken off for a wrong answer. If Adam's score in the exam is between \(45\) and \(80\) exclusive, what is the difference between the maximum possible number of right answers \((M)\) and minimum possible number of right answers \((m)?\)

A pair of jeans at Kim's Clothing which was priced \(30\)% above the merchant's cost is now on sale for \(20\)% off. At the sale price, the profit margin per unit is at least $\(7\). If the merchant's cost of a pair of jeans is at least $\(x\), what is \(x\)?

Let \(200n(400-n)\) represent the total revenue (in dollars) of a company from selling \(n\) units of the machine they produce, where \(0\le n \le 200.\) If it costs \(30000\) dollars to produce one unit of the machine and the company wants their profit to be at least \(2625000\) dollars, what is the range of the number of units they need to sell?

The results of Richard's first two math tests are \(81\) and \(84\) points, respectively. What is the minimum score he can achieve on the third test in order to obtain an average of at least \(84\) points for all three tests?

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