Question

Solve the equation: 6x+2 = 9x-4

Answer 1

To solve the equation
`\(6x+2 = 9x-4\)`, we first need to simplify and combine like terms. Subtracting (6x) from both sides and adding 4 to both sides, we get
`\(2 = 3x - 4\)`. Next, adding 4 to both sides, we have (6 = 3x). Finally, dividing both sides by 3, we find
`\(x = (6)/(3)\)`.

Step-by-step explanation:

In order to solve the equation (6x+2 = 9x-4), we start by simplifying and combining like terms. First, subtracting (6x) from both sides yields
`\(2 = 3x - 4\)`. To isolate the variable term, we then add 4 to both sides, resulting in (6 = 3x). Finally, to find the value of (x), we divide both sides by 3, yielding
`\(x = (6)/(3)\)`.

This simplifies further to (x = 2), representing the solution to the original equation. Breaking down the steps, the initial manipulation aims to gather all (x)-related terms on one side of the equation. The subsequent addition of 4 on both sides is a means of isolating the term with (x).

The final step, division by 3, is applied to find the value of (x). Each step follows the principles of maintaining equation balance by performing equivalent operations on both sides.

Answer 2

The solution to the equation 6x + 2 = 9x - 4 is x = 2.

Step-by-step explanation:

To solve the equation 6x + 2 = 9x - 4, we want to isolate x on one side of the equation. First, let's gather x terms on one side by subtracting 6x from both sides, resulting in 2 = 3x - 4. Next, add 4 to both sides to isolate the term with x: 2 + 4 = 3x, giving us 6 = 3x. Now, divide both sides by 3 to solve for x: x = 6 ÷ 3 = 2.

This process involves simplifying the equation step by step to isolate the variable x. Initially, moving terms with x to one side and constant terms to the other helps in getting an equation in terms of x. By performing inverse operations like addition, subtraction, multiplication, and division, the goal is to isolate x to determine its value. In this case, the solution is x = 2, which satisfies the given equation when substituted back into the original equation: 6x + 2 = 9x - 4.