Question

Solve 4(x - 3) - 2(x - 1) > 0. (10 points)

1. (x | x < -5)
2. (x | x > -5)
3. (x | x > 5)
4. (x | x < 5)​

Answer 1

3. (x | x > 5)

Explanation:

To solve this inequality, we need to isolate the variable on one side and the constant on the other side. To do this, we need to use the properties of inequalities and the order of operations to manipulate the given inequality into a form we can solve.

First, we need to distribute the coefficients in front of the parentheses on the left-hand side of the inequality. This gives us:

4x - 12 - 2x + 2 > 0

Next, we can combine like terms on the left-hand side of the inequality by adding the terms with the variable and subtracting the constant terms. This gives us:

2x - 10 > 0

Now, we have isolated the variable on one side of the inequality and the constant on the other side. To solve the inequality, we need to determine the values of x that make the inequality true.

To do this, we can divide both sides of the inequality by the coefficient of the variable, which gives us:

x - 5 > 0

This inequality is satisfied when x is greater than 5. Therefore, the solution to the original inequality is x > 5.