Question

u2l20 practice - writing and solving inequalities in one variable
possible points: 1
a cell phone company offers two texting plans. people who use plan a pay 10 cents for each text sent or received. people who use plan b pay 12 dollars per month, and then pay an additional 2 cents for each text sent or received.
1 write an inequality to represent the fact that it is cheaper for someone to use plan a than plan b. use x to represent the number of texts they send.
2 solve the inequality.
$x < 1.5$ $x > 1.5$ $x < 150$ $x > 150$ $10x > 12 + 2x$ $10x < 12 + 2x$ $0.1x < 12 + 0.02x$ $0.1x > 12 + 0.02x$

Explanation:

Step1: Write cost expressions

For plan A, cost is \(0.1x\) (since 10 cents = \(0.1\) dollars). For plan B, cost is \(12 + 0.02x\) (12 dollars fixed plus 2 cents per text, 2 cents=\(0.02\) dollars).

Step2: Form the inequality

Since plan A is cheaper, \(0.1x<12 + 0.02x\).

Step3: Solve the inequality

Subtract \(0.02x\) from both sides: \(0.1x-0.02x<12+0.02x - 0.02x\), so \(0.08x<12\).
Divide both sides by \(0.08\): \(x<\frac{12}{0.08}\), \(x < 150\).

Answer:

1. \(0.1x<12 + 0.02x\)
2. \(x < 150\)