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Define a variable and write an inequality for each problem and then solve.

45. Twice the sum of a number and 5 is no more than 3 times that same number increased by 11.

Short Answer

Expert verified

The inequality is:2x+5≤3x+11

Value of the number is x≥-1

Step by step solution

01

- Define the variable.

A variable is a term that is used to represent an unknown value.

02

- Write the inequality.

From given, let the number added to 5 be x.

As twice the sum is no more than 3 times x increased by 11.

So, the inequality is:

2x+5≤3x+11

03

- Solve the inequality.

To simplify this inequality, use subtraction property

2x+5≤3x+112x+10≤3x+1110−11≤3x−2xx≥−1

Therefore, the inequality is 2x+5≤3x+11 and the value of x is x≥-1.

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In 1950, the average price of a car was about \(2000. This may sound inexpensive, but the average income in 1950 was much less than it is now. To compare dollar amounts over time, use the formula V=ASC, where A is the old dollar amount, S is the starting year’s Consumer price index (CPI), C is the converting year’s CPI, and V is the current value of the old dollar amount. Buying a car for \)2000in 1950 was like buying a car for how much money in 2000?

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