Question

Simplify 2(3x - 9) = 6x - 18.

Answer 1

The equation (2(3x - 9) = 6x - 18) has infinitely many solutions, implying that any real number can be substituted for (x) and satisfy the equation.

Step-by-step explanation:

To simplify (2(3x - 9) = 6x - 18), start by distributing the 2 outside the parentheses to everything inside:

`\[2 * 3x - 2 * 9 = 6x - 18\]`

[6x - 18 = 6x - 18]

After distributing, notice that both sides of the equation are identical: (6x - 18 = 6x - 18). This means that any value of x will satisfy this equation. However, in algebra, when both sides are the same, it implies that the equation is an identity, and there are infinite solutions, not just one.

Upon further examination, if you subtract (6x) from both sides of the equation, you get (-18 = -18), which is a true statement. This indicates that any value of x can be substituted into the equation, making it true. Consequently, this equation has infinitely many solutions.

However, in terms of solving for (x), when you subtract (6x) from both sides, you are left with (-18 = -18), which is always true, irrespective of the value of (x).

Thus, the solution is that (x) can be any real number. In this particular equation, (x = 0) is one of the infinite solutions.