Final answer:
To find the solution for x in the equation -2x + 6 = -(2/3)x + 5, we first eliminate the fraction and isolate the x term, which gives us x = 3/4 as the solution.
Step-by-step explanation:
To solve the equation -2x + 6 = -(2/3)x + 5, we start by eliminating the fractions and aiming to get all terms containing x on one side of the equation and the constants on the other. Multiplying both sides by 3 to remove the fraction gives us -6x + 18 = -2x + 15.
Next, we add 6x to both sides to get all the x terms on one side:
18 = 4x + 15.
We then subtract 15 from both sides to isolate the x term:
3 = 4x.
To find the value of x, we divide both sides by 4:
x = 3/4.
This is the solution for x. The process we used involved simple algebraic steps of combining like terms and manipulating the equation to isolate the variable x.