Question

What value of x is in the solution set of the inequality 2(3x-1)>4x-6

Answer 1

Answer: the solution set of the inequality 2(3x-1)>4x-6 is all values of x greater than -2.

Step-by-step explanation: To solve the inequality 2(3x-1)>4x-6, we first simplify the left side by distributing the 2, which gives us 6x-2. Substituting this back into the original inequality, we get:

6x-2 > 4x-6

Next, we isolate the variable term (6x) by subtracting 4x from both sides:

2x-2 > -6

Then, we add 2 to both sides to isolate the variable term completely:

2x > -4

Finally, we divide both sides by 2 to solve for x:

x > -2

Therefore, the solution set of the inequality 2(3x-1)>4x-6 is all values of x greater than -2.

Answer 2

The value of x that satisfies the inequality 2(3x-1)>4x-6 is any number greater than -2. To find this, we simplify and rearrange the inequality to isolate and solve for x.

Step-by-step explanation:

To solve the inequality 2(3x-1)>4x-6, we first expand the left side and simplify the equation.

1. Multiply the 2 with each term inside the parentheses: 2 × 3x = 6x and 2 × (-1) = -2, giving us 6x - 2.
2. So the inequality now looks like 6x - 2 > 4x - 6.
3. To solve for x, we move all terms containing x to one side by subtracting 4x from both sides, yielding 2x - 2 > -6.
4. Next, we isolate x by adding 2 to each side, resulting in 2x > -4.
5. Lastly, we divide both sides by 2 to solve for x, which gives us x > -2.

Therefore, the solution set for the inequality 2(3x-1)>4x-6 is x > -2.