Chapter 2: Q.30. (page 111)

Solve the linear equation $10 [5 (n + 1) + 4 (n - 1)] = 11 [7 (5 + n) - (25 - 3 n)]$ .

Short Answer

Expert verified

The solution is $n = - 5$ .

Step by step solution

Step 1. Given information.

The given equation is $10 [5 (n + 1) + 4 (n - 1)] = 11 [7 (5 + n) - (25 - 3 n)]$ .

Step 2. Simplify inner most parenthesis first.

$10 [5 (n + 1) + 4 (n - 1)] = 11 [7 (5 + n) - (25 - 3 n)] 10 [5 n + 5 + 4 n - 4] = 11 [35 + 7 n - 25 + 3 n]$

Combine like terms in the braces.

$10 [9 n + 1] = 11 [10 + 10 n]$

Step 3. Apply the distributive property to simplify the equation.

Simplify each side of the equation.

$10 \times 9 n + 10 = 11 \times 10 + 11 \times 10 n 90 n + 10 = 110 + 110 n$

Step 4. Collect all variables terms on other side of the equation.

Subtract $110 n$ from each side.

$90 n + 10 - 110 n = 110 + 110 n - 110 n - 20 n + 10 = 110$

Step 5. Collect all constant terms on other side of the equation and then simplify.

Subtract $10$ from each side.

$- 20 n + 10 - 10 = 110 - 10 - 20 n = 100$

Divide each side by $- 20$ .

$\frac{- 20 n}{- 20} = \frac{100}{- 20} n = - 5$

Hence, the required solution of the given equation is $n = - 5$ .

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Solve the linear equation $10 [5 (n + 1) + 4 (n - 1)] = 11 [7 (5 + n) - (25 - 3 n)]$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify inner most parenthesis first.

Step 3. Apply the distributive property to simplify the equation.

Step 4. Collect all variables terms on other side of the equation.

Step 5. Collect all constant terms on other side of the equation and then simplify.

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Solve the linear equation105n+1+4n-1=1175+n-25-3n.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify inner most parenthesis first.

Step 3. Apply the distributive property to simplify the equation.

Step 4. Collect all variables terms on other side of the equation.

Step 5. Collect all constant terms on other side of the equation and then simplify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

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Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve the linear equation $10 [5 (n + 1) + 4 (n - 1)] = 11 [7 (5 + n) - (25 - 3 n)]$ .