Which value of x is the solution set of 2(3x-1)≥4x-6

-1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of Equality

Step-by-step explanation:

Step 1: Define

2(3x - 1) ≥ 4x - 6

Step 2: Solve for x

Distribute 2:                                 6x - 2 ≥ 4x - 6Subtract 4x on both sides:          2x - 2 ≥ -6Add 2 on both sides:                   2x ≥ -4Divide 2 on both sides:               x ≥ -2

Here we see that any value x greater than or equal to -2 would work as a solution.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!