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Chapter 3: Q1C. (page 127)

Solve the equation. Check your solution.

5n-2=3n+6

Short Answer

Expert verified

The solution for the equation5n鈭�2=3n+6 isn=4 .

Step by step solution

01

– Separate the variable and constants

Write the original equation and separate the variable and constants.

5n鈭�2=3n+65n鈭�2鈭�5n=3n+6鈭�5n[Substract5nfromeachside.]鈭�2=鈭�2n+6[Simplify.]鈭�2鈭�6=鈭�2n+6鈭�6[Subtract6fromeachside.]鈭�8=鈭�2n[Simplify.]

02

– Solve for n

Now, divide both sides of the equation by 2.

鈭�82=鈭�2n2n=4

Therefore, the solution of the equation is n=4.

03

– Check the solution

To check the solution, write the original equation and substitute the value of n.

5n鈭�2=3n+6

Now, substitute n=4and check the result.

5(4)鈭�2=3(4)+620鈭�2=12+618=18

As the left-hand side is equal to right hand side, this signifies that the solution is correct.

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