(2x+2)/4 = (x-3)/3

Question: What is the solution to the equation (2x+2)/4 = (x-3)/3?

1. x = 17/36
2. x = 13.500
3. x = 27/2
4. x = -0.637 or x = 3.137

Answer: (A) x = 17/36

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(2x+2)/4 = (x-3)/3 Solution:

We can multiply both sides by the least common multiple of the denominators, which is 12. This gives us:

3(2x+2) = 4(x-3)
6x+6 = 4x-12
2x = -18
x = -9

However, this solution is extraneous, as the original equation is undefined when x = 2. To find the correct solution, we can multiply both sides of the original equation by 4:

2x+2 = 4(x-3)
2x+2 = 4x-12
-2x = -14
x = 7

This solution satisfies the original equation, so it is the correct solution. Therefore, the solution is x = 17/36.

To solve the equation $(2x+2)/4=(x-3)/3$, we begin by eliminating the denominators. Multiply both sides by 12, the least common multiple of 4 and 3. This gives $12\times (2x+2)/4=12\times (x-3)/3$.

Simplifying, we get $3(2x+2)=4(x-3)$. Expanding both sides, it becomes $6x+6=4x-12$. Subtract $4x$ from both sides, resulting in $2x+6=-12$. Subtract 6 from both sides to get $2x=-18$, and dividing by 2, $x=-9$. Therefore, the solution to the equation is $x=-9$.

Solution to the quadratic equation 4x ^ 2 – 5x – 12 = 0?

We can use the quadratic formula to solve the quadratic equation 4x ^ 2 – 5x – 12 = 0. The standard form of the quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0, where $a=4$, $b=-5$, and $c=-12$. The quadratic formula is:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}x=2a−b±b2−4ac​​

Substitute the values of $a$, $b$, and $c$ into the formula:

x=−(−5)±(−5)2−4(4)(−12)2(4)x = \frac{-(-5) \pm \sqrt{(-5)^2 – 4(4)(-12)}}{2(4)}x=2(4)−(−5)±(−5)2−4(4)(−12)​​

Solving this gives the roots of the equation 4×2−5x−12=04x^2 – 5x – 12 = 04x2−5x−12=0.