In the equation 6x=4(x-2), x is -4.
We are given an algebraic equation and the task to solve for its one variable, x.
To solve for x in the equation, we aim to isolate x on one side of the equals sign. We can do this by manipulating both sides of the equation until we achieve this result.
On the right side of the equation, we see the expression 4(x-2). To begin simplifying, we need to distribute the 4 to the (x-2).
To do this, we will multiply 4 by x and 4 by -2 to get a new expression for the right side of the equation.
[tex]4(x-2)=(4\cdot x)+(4\cdot(-2))=4x+(-8)=4x-8[/tex]
This gives us a new equation of 6x=4x-8.
To isolate x, we need to remove it on the right side by subtracting 4x.
Remember: Whatever you do on one side of the equation, do the same on the other.
This means we will subtract 4x from each side of the equation, leaving us with a new equation of 2x=-8.
Finally, to completely isolate x, we can divide both sides of the equation by 2, canceling out the coefficient on the left side.
This leaves us with a final equation of x=-4.
Now that we know the value of x is -4, we can check the answer by substituting it back into the original equation:
[tex]6(-4)=4(-4-2)[/tex]
Simplify to ensure the equation is correct:
[tex]-24=4(-6)[/tex]
[tex]-24=-24[/tex]
Learn more about solving for a variable in an algebraic equation at https://brainly.com/question/30114755.
Answer:
Step-by-step explanation:
Multiply 4 with x and then with 2, to remove the parenthesis;
6x=4x-8
6x-4x=-8
2x=-8
x=-8/2
x=-4