Question

1. lin is solving the inequality ( 15 - x < 14 ). she knows the solution to the equation ( 15 - x = 14 ) is ( x = 1 ). how can lin determine whether ( x > 1 ) or ( x < 1 ) is the solution to the inequality?
2. 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.

a. 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.
b. solve the inequality.

1. clare made an error when solving ( -4x + 3 < 23 ).

( -4x + 3 < 23 )
( -4x < 20 )
( x < -5 )
describe the error that she made.

Explanation:

Step1: Solve inequality for plan A and plan B

Plan A cost: \(10x\) cents. Plan B cost: \(1200 + 2x\) cents (since \(12\) dollars \(= 1200\) cents).
The inequality for plan A being cheaper is \(10x<1200 + 2x\).

Step2: Solve the inequality

Subtract \(2x\) from both sides: \(10x-2x<1200+2x - 2x\), so \(8x<1200\).
Divide both sides by \(8\): \(x < 150\).

Answer:

a. \(10x<1200 + 2x\)
b. \(x < 150\)