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