Chapter 2: Q321. (page 184)

Solve the equality, graph the solution on the number line and express the solution in the interval notation.
$6 n - 12 (3 - n) \leq 9 (n - 4) + 9 n$

Short Answer

Expert verified

Indentity

$(- \infty, \infty)$

Step by step solution

Step 1. Given information.

The given inequality is

$6 n - 12 (3 - n) \leq 9 (n - 4) + 9 n$

Step 2. Solving the inequality.

Distributing and combining like terms:

$6 n - 36 + 12 n \leq 9 n - 36 + 9 n = > 18 n - 36 \leq 18 n - 36$

Subtracting both sides by $18 n - 36$ :

$18 n - 36 - (19 n - 36) \leq 18 n - 36 - (18 n - 36)$

Simplifying

$0 \leq 0$

Since the variables ( $n$ ) are gone and we have a true statement, the inequality is an identity and the solution is all real numbers.

Step 3. Graphing the solution on the number line.

The graph of the solution on the number line is presented below:

Step 4. Writing the solution in the interval notation.

In the interval notation, the solution can be expressed as

$(- \infty, \infty)$

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Solve the equality, graph the solution on the number line and express the solution in the interval notation.
$6 n - 12 (3 - n) \leq 9 (n - 4) + 9 n$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving the inequality.

Step 3. Graphing the solution on the number line.

Step 4. Writing the solution in the interval notation.

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Solve the equality, graph the solution on the number line and express the solution in the interval notation.6n-123-n≤9n-4+9n

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving the inequality.

Step 3. Graphing the solution on the number line.

Step 4. Writing the solution in the interval notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve the equality, graph the solution on the number line and express the solution in the interval notation.
$6 n - 12 (3 - n) \leq 9 (n - 4) + 9 n$