Question

3(4 – 2x) = x + 5(x - 2)
How many solutions are possible for the equation?

Answer 1

The given equation has only one solution.

Step-by-step explanation:

The equation
`\(3(4 - 2x) = x + 5(x - 2)\)`can be solved to find the value of x. First, distribute the terms within the parentheses to simplify the equation:

`\[12 - 6x = x + 5x - 10\]`

Combine like terms on both sides:

`\[12 - 6x = 6x - 10\]`

Now, move all x-related terms to one side and constants to the other side:

`\[12 + 10 = 6x + 6x\]`

`\[22 = 12x\]`

Finally, solve for x:

`\[x = (22)/(12) = (11)/(6)\]`

The equation
`\(3(4 - 2x) = x + 5(x - 2)\)` has one solution, which is
`\(x = (11)/(6)\)`. This conclusion is reached through systematic algebraic manipulation, ensuring accuracy in the solution. The value of x makes both sides of the equation equal, satisfying the given mathematical expression.