What value of x makes this equation true?
1/3(9x-2)+1=2(4x+1)
a) x=-3 b)x=-1/3 c)x=1/3 d)x=3
Please explain. Having a hard time figuring out.
1/3 (9x-2) + 1 = 2(4x+1)
You can multiply by 3 to get
9x-2 + 3 = 6(4x+1)
9x+1 = 24x+6
-5 = 15x
x = -1/3
Thank you
To solve this equation, we need to simplify it step by step.
Given equation: 1/3(9x-2) + 1 = 2(4x + 1)
Step 1: Distribute the 1/3 to the terms inside the parenthesis:
(1/3) * (9x - 2) + 1 = 2(4x + 1)
(9/3)x - (2/3) + 1 = 2(4x + 1)
3x - (2/3) + 1 = 2(4x + 1)
3x - (2/3) + 1 = 8x + 2
Step 2: Combine like terms on both sides of the equation:
3x - (2/3) + 1 = 8x + 2
3x - (2/3) + (3/3) = 8x + 2
3x + (1/3) = 8x + 2
Step 3: Move variables to one side and constants to the other side:
3x + (1/3) - 8x = 8x + 2 - 8x
-5x + (1/3) = 2
Step 4: Isolate the variable by subtracting (1/3) from both sides of the equation:
-5x + (1/3) - (1/3) = 2 - (1/3)
-5x = 2 - (1/3)
-5x = 6/3 - 1/3
-5x = 5/3
Step 5: Solve for x by dividing both sides of the equation by -5:
(-5x)/-5 = (5/3)/-5
x = -1/3
Therefore, the value of x that makes the equation true is x = -1/3. So the answer is (b) x = -1/3.
To find the value of x that makes the equation true, we need to solve for x. Let's go through the steps one by one:
1. Begin by distributing on both sides of the equation. On the left side, distribute the 1/3 to (9x - 2):
(1/3)(9x - 2) + 1 = 2(4x + 1)
This simplifies to:
(3x - 2/3) + 1 = 8x + 2
2. Next, combine like terms. On the left side, combine the (3x - 2/3) and 1:
3x - 2/3 + 1 = 8x + 2
Combine the numbers and fractions on the left side:
3x + 1/3 = 8x + 2
3. Move all the terms containing x to one side by subtracting 8x from both sides:
3x - 8x + 1/3 = 2
This simplifies to:
-5x + 1/3 = 2
4. To eliminate the fraction, multiply through the entire equation by 3:
3 * (-5x + 1/3) = 3 * 2
This becomes:
-15x + 1 = 6
5. Subtract 1 from both sides to isolate the term with x:
-15x = 6 - 1
Simplifying further:
-15x = 5
6. Divide both sides of the equation by -15 to solve for x:
x = 5 / -15
This can be simplified as:
x = -1/3
Therefore, the correct answer is b) x = -1/3.