Question

2/3(x+3)+3/4(x-1)=14​

Answer 1

Ответ:

Пошаговое объяснение:

2/3(x+3)+3/4(x-1)=14​

2/3x + 2 + 3/4x - 3/4 = 14    | *12

8x + 24 + 9x - 9 = 168

17x + 15 = 168

17x = 168 - 15

17x = 153

x = 153 : 17

x = 9

Answer 2

To solve the equation $\frac{2}{3}(x+3) + \frac{3}{4}(x-1) = 14$, we need to find the value of $x$ that satisfies the equation. To do this, we'll first simplify the equation by clearing the fractions and then solve for $x$.

Step 1: Clear the fractions. To clear the fractions, we need to find the least common multiple (LCM) of the denominators, which is $3 \times 4 = 12$. Multiply both sides of the equation by 12 to eliminate the fractions:

$12 \times \left( \frac{2}{3}(x+3) \right) + 12 \times \left( \frac{3}{4}(x-1) \right) = 12 \times 14$

Step 2: Simplify the equation. On the left side, the denominators will cancel out, and we will be left with:

$4(x+3) + 3(x-1) = 168$

Step 3: Distribute and combine like terms. Expand the brackets:

$4x + 12 + 3x - 3 = 168$

Combine like terms:

$7x + 9 = 168$

Step 4: Isolate $x$ on one side. To isolate $x$ on one side of the equation, we'll move the constant term to the other side. Subtract 9 from both sides:

$7x = 168 - 9$

$7x = 159$

Step 5: Solve for $x$. Finally, divide both sides by 7 to solve for $x$:

$x = \frac{159}{7}$

$x \approx 22.71$

Therefore, the solution to the equation is $x \approx 22.71$.