Question

6) 3 + (x - 7)/4 = (2x + 5)/3

Answer 1

Ответ:

Приведем к общему знаменателю получим

4*3/4+x-7/4=(2x+5)/3

Сложим дроби и перемножим

12x+x-7/4=(2x+5)/3

3x(x+5)=4(2x+5)

3x=8x+5

-5x=5 | -5

x=-1

Пошаговое объяснение:

Answer 2

To solve the equation 3 + (x - 7)/4 = (2x + 5)/3, we'll follow these steps:

Step 1: Simplify the equation by getting rid of the fractions. Step 2: Solve the resulting linear equation. Step 3: Verify the solution.

Let's solve it step by step:

Step 1: Simplify the equation by getting rid of the fractions. To eliminate the fractions, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 12. Multiplying every term in the equation by 12, we get:

12 * (3 + (x - 7)/4) = 12 * (2x + 5)/3

Simplifying the equation further:

36 + 3(x - 7) = 4(2x + 5)

Step 2: Solve the resulting linear equation. Distribute the coefficients on both sides:

36 + 3x - 21 = 8x + 20

Combine like terms:

3x + 15 = 8x + 20

Move the variables to one side and the constants to the other side:

3x - 8x = 20 - 15

-5x = 5

Divide both sides of the equation by -5:

x = -1

Step 3: Verify the solution. Substitute the value of x = -1 back into the original equation:

3 + (-1 - 7)/4 = (2(-1) + 5)/3

Simplifying the equation:

3 + (-8)/4 = (-2 + 5)/3

3 - 2 = 3/3

1 = 1

Since the left side of the equation equals the right side when x = -1, we can conclude that x = -1 is the solution to the equation.

Therefore, the solution to the equation 3 + (x - 7)/4 = (2x + 5)/3 is x = -1.