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Chapter 0: Problem 50

Solve each compound inequality. $$7

Short Answer

Expert verified
The solution to the compound inequality is \(2 < x < 6\)

Step by step solution

01

Identify the inequalities

The exercise presents a compound inequality which can be broken down into two inequalities: \(7 < x + 5\) and \(x + 5 < 11\). These can be handled separately.
02

Solve the first inequality

To find the value of 'x' in the first inequality \(7 < x + 5\), subtract 5 from both sides of the inequality. This simplifies to \(2 < x\). This shows that 'x' is greater than 2.
03

Solve the second inequality

To find the value of 'x' in the second inequality \(x + 5 < 11\), also subtract 5 from both sides of the inequality. This simplifies to \(x < 6\). This indicates that 'x' is less than 6.
04

Combine the results

Combining the results of the two inequalities provides a range for the values of 'x'. This gives \(2 < x < 6\). This means that possible values of 'x' are greater than 2 and less than 6.

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Most popular questions from this chapter

Explain how to solve \(x^{2}+6 x+8=0\) using the quadratic formula.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \((2 x-3)^{2}=25\) is equivalent to \(2 x-3=5\).

What is a linear equation in one variable? Give an example of this type of equation.

Explain how to add or subtract rational expressions with the same denominators.

Exercises \(142-144\) will help you prepare for the material covered in the next section. Use the distributive property to multiply: $$ 2 x^{4}\left(8 x^{4}+3 x\right) $$
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