Chapter 1: Q72. (page 39)

Solve each equation. Check the solution.
$|x + 4| + 3 = 17$

Short Answer

Expert verified

The value of $x$ is $10$ .

Step by step solution

- State the definition of absolute value.

The distance of a number from 0 in the number line is called the absolute value and since distance cannot be negative so absolute value is always positive.

- Solve the inequality.

If x is a number, then absolute value of x is written as $|x|$ .

Here, the inequality is:

$|x + 4| + 3 = 17$

Case 1:

\begin{matrix} a = b \\ x + 4 + 3 = 17 \\ x + 7 = 17 \\ x + 7 - 7 = 17 - 7 \\ x = 10 \end{matrix}

Or Case 2:

\begin{matrix} a = - b \\ x + 4 + 3 = - 17 \\ x + 7 = - 17 \\ x + 7 - 7 = - 17 - 7 \\ x = - 24 \end{matrix}

The solution is $10$ and $- 24$ .

- Check the solution.

For case 1: $x = 10$ .

Check:

\begin{array}{r} |x + 4| + 3 = 17 \\ |10 + 4| + 3 = 17 \\ |14| + 3 = 17 \\ 14 + 3 = 17 \\ 17 = 17 \end{array}

Thus, it is correct.

For case 2: $x = - 24$ .

Check:

\begin{array}{r} |x + 4| + 3 = 17 \\ |- 24 + 4| + 3 = 17 \\ |- 20| + 3 = 17 \\ 20 + 3 = 17 \\ 23 = 17 \end{array}

Thus, it is not correct.

For $x = - 24$ , the soultion is not correct.

- State the conclusion.

Since, $23 \neq 17$ that is for $x = - 24$ , the soultion is not correct, then there is only one that is 10. Therefore, the solution set for x is $\{10\}$ .

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Solve each equation. Check the solution.
$|x + 4| + 3 = 17$

Short Answer

Step by step solution

- State the definition of absolute value.

- Solve the inequality.

- Check the solution.

- State the conclusion.

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Solve each equation. Check the solution.x+4+3=17

Short Answer

Step by step solution

- State the definition of absolute value.

- Solve the inequality.

- Check the solution.

- State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Theoretical and Mathematical Physics

Discrete Mathematics

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Solve each equation. Check the solution.
$|x + 4| + 3 = 17$