which value for x makes the equation true x-6=3(x-5/2)+1
x-6=3(x-5/2)+1
x-6 = 3x - 15/2 + 1
-2x = 6-15/2 + 1 = 1/2
x = 1/4
1/4
To find the value of x that makes the equation true, you need to solve the equation step by step. Let's break it down:
x - 6 = 3(x - 5/2) + 1
Step 1: Distribute the 3 to both terms inside the parentheses:
x - 6 = 3x - 15/2 + 1
Step 2: Simplify the equation by combining like terms:
x - 6 = 3x - 15/2 + 2/2
Step 3: Convert the constant terms to fractions with a common denominator:
x - 6 = 3x - 13/2
Step 4: Move all the x terms to one side of the equation and the constant terms to the other side to isolate the variable x. You can do this by subtracting x from both sides:
x - x - 6 = 3x - x - 13/2
Simplifying further:
-6 = 2x - 13/2
Step 5: Move all the constant terms to one side by adding 13/2 to both sides:
-6 + 13/2 = 2x - 13/2 + 13/2
Simplifying:
-12/2 + 13/2 = 2x
1/2 = 2x
Step 6: Divide both sides by 2 to solve for x:
(1/2) / 2 = (2x) / 2
1/4 = x
Therefore, the value of x that makes the equation true is x = 1/4.