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Twice a​ number, increased by one​, is between negative three and seven. find all the numbers.

User Danno
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Final answer:

To solve the inequality -3 < 2x + 1 < 7 for the number x, subtract 1 from all parts and then divide by 2. The solution is the range of numbers greater than -2 and less than 3.

Step-by-step explanation:

The problem statement here results in an inequality that can be expressed algebraically. If 'x' represents the unknown number, we can write the inequality as -3 < 2x + 1 < 7.

To solve for 'x', we will isolate the variable on one side by following the rules of inequalities similar to solving equations.

First, subtract 1 from all parts of the inequality to get the pure inequality without a constant.

-4 < 2x < 6

Now, divide all parts of the inequality by 2, which yields:

-2 < x < 3

All numbers greater than -2 and less than 3 satisfy the original problem statement. Therefore, the range of numbers that solve the inequality is from -2 to just below 3.

User Anjsimmo
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