Solve for x 8+6x=8+8x+7+3
The question provided is an algebraic equation requiring the solution for the variable 'x'. It involves simplifying the equation by performing basic arithmetic operations such as addition and subtraction, and isolating the variable 'x' on one side of the equation to find its value. The goal is to determine what number 'x' represents to make the equation true.
$8 + 6 x = 8 + 8 x + 7 + 3$
Answer
Solution:
Step 1: Combine like terms on the right side of the equation.
Combine $8$ and $7$ to get $15$.
Add $15$ to $3$ to obtain $18$.
Thus, the equation becomes $8 + 6x = 8x + 18$.
Step 2: Isolate the variable terms on one side.
Subtract $8x$ from both sides to move the variable terms to one side.
This results in $8 + 6x - 8x = 18$, simplifying to $8 - 2x = 18$.
Step 3: Move the constant terms to the opposite side.
Subtract $8$ from both sides to isolate the terms with $x$.
The equation now reads $-2x = 18 - 8$, which simplifies to $-2x = 10$.
Step 4: Solve for $x$.
Divide both sides of the equation by $-2$ to solve for $x$.
This yields $x = \frac{10}{-2}$.
Simplifying the fraction gives $x = -5$.
Knowledge Notes:
To solve a linear equation, we typically follow these steps:
Combine like terms: Simplify each side of the equation by combining like terms, which are terms that have the same variables raised to the same power.
Isolate the variable: Move all the terms containing the variable to one side of the equation and the constant terms to the other side. This is usually done by adding or subtracting terms from both sides of the equation.
Solve for the variable: Once the variable terms are isolated on one side, you can solve for the variable by performing operations that will get the variable by itself. If the variable term is multiplied by a number, you can divide both sides by that number. If it's divided by a number, you can multiply both sides by that number.
Check your solution: It's always a good practice to check your solution by plugging it back into the original equation to ensure that it satisfies the equation.
In the context of the given problem, the equation is first simplified by combining like terms. Then, terms containing $x$ are moved to one side, and constants to the other, to isolate $x$. Finally, the equation is solved for $x$ by dividing both sides by the coefficient of $x$. The solution is checked by substituting back into the original equation.
