GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A manufacturing company's production cost, C, in thousands of dollars, depends on the number of units, x, produced according to the function C(x) = 0.5x + 10. The company wants to keep its production cost below $25,000. Which inequality represents the number of units the company can produce?
- Ax < 30
- Bx < 50
- Cx < 10
- Dx < 70
Show answer & explanationAnswer & explanation
Correct answer: A. x < 30
The cost function is C(x) = 0.5x + 10. The company wants the cost to be below $25,000. Since C(x) is in thousands of dollars, $25,000 is 25. So, we set up the inequality: 0.5x + 10 < 25. Subtract 10 from both sides: 0.5x < 15. Divide by 0.5: x < 30. The company can produce fewer than 30 units.
Why the other options are wrong
- B. Incorrect. This would mean 0.5x < 25, which implies 0.5x+10 < 35.
- C. Incorrect. This would mean 0.5x < 5, which implies 0.5x+10 < 15.
- D. Incorrect. This would mean 0.5x < 35, which implies 0.5x+10 < 45.
Solving Linear Inequalities
Solving a linear inequality involves finding the range of values for a variable that make the inequality true. The process is similar to solving linear equations, with one key difference: multiplying or dividing by a negative number reverses the inequality sign.
- Isolate the variable using inverse operations.
- If you multiply or divide both sides by a negative number, flip the inequality sign.
- The solution is a range of values, often represented on a number line or in interval notation.
Memory trick: Balance the scale, flip if you negate!