Chapter 1: Q61. (page 39)

Solve each equation. Check the solution.
61. If $|x + 1| = x$

Short Answer

Expert verified

There isno solution set for $x$ .

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:

$|x + 1| = x$

Case 1:

$\begin{matrix} a = b \\ x + 1 = x \\ x + 1 - 1 = x - 1 \\ x = x - 1 \end{matrix}$

Here value of cannot be determined.

Or Case 2:

$\begin{matrix} a = - b \\ x + 1 = - x \\ x + 1 - 1 = - x - 1 \\ x + x = - x - 1 + x \\ 2 x = - 1 \\ x = - 0.5 \end{matrix}$

The solution is $- 0.5$ . Here x has only one value.

- Check the solution.

For case 2: $x = - 0.5$ .

Check:

\begin{array}{l} |x + 1| = x \\ |- 0.5 + 1| = - 0.5 \\ |0.5| = - 0.5 \\ 0.5 = - 0.5 \end{array}

Thus, it is not correct that is $x = - 0.5$ is not a solution.

- State the conclusion.

Therefore, there is no solution set for x.

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Solve each equation. Check the solution.
61. If $|x + 1| = x$

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.61. If x+1=x

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

Geometry

Mechanics Maths

Decision Maths

Logic and Functions

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve each equation. Check the solution.
61. If $|x + 1| = x$