Determine whether the given solution is correct. If it is not,find the solution. A) Is 11 a solution for 7x+6-3x=2x-5+x?

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embizze | High School Teacher | (Level 1) Educator Emeritus

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To determine if the given number is a solution to an equation, we substitute in place of the variable. If the resulting statement is true, the number is a solution.

Given 7x+6-3x=2x-5+x   Check 11:

7(11)+6-3(11)=77+6-33=50

2(11)-5+11=22-5+11=28

Since the right hand side is not equal to the left hand side, 11 is not a solution.

To find the correct solution, we perform the following algebraic steps:

On both sides of the equation we collect like terms; then we add/subtract so that the variable is on one side of the equation; then we add/subtract so that the term with the variable is isolated; then we multiply/divide so that the variable is isolated.

7x+6-3x=2x-5+x  Add like terms (Collect like terms)

4x+6=3x-5           Subtract 3x from both sides of the equation

x+6=-5                Subtract 6 from both sides of the equation

x=-11

The solution is x=-11

Check: 7(-11)+6-3(-11)=-77+6+33=-38

2(-11)-5+(-11)=-22-5-11=-38

Since both sides of the equation are the same, x=-11 is a solution.

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