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Chapter 2: Q.30. (page 111)

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

Short Answer

Expert verified

The solution isn=-5.

Step by step solution

01

Step 1. Given information.

The given equation is105n+1+4n-1=1175+n-25-3n.

02

Step 2. Simplify inner most parenthesis first.

105n+1+4n-1=1175+n-25-3n105n+5+4n-4=1135+7n-25+3n

Combine like terms in the braces.

109n+1=1110+10n

03

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

Simplify each side of the equation.

10脳9n+10=11脳10+11脳10n90n+10=110+110n

04

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

Subtract 110nfrom each side.

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

05

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

Subtract 10from each side.

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

Divide each side by -20.

-20n-20=100-20n=-5

Hence, the required solution of the given equation isn=-5.

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