Question

5/6*(x+3)+1/4(x-1)=12

Answer 1

Добрый день. Надеюсь все понятно.

Answer 2

To solve the equation $\frac{5}{6}(x+3) + \frac{1}{4}(x-1) = 12$, we'll follow these steps:

Step 1: Distribute the fractions. Step 2: Combine like terms. Step 3: Isolate the variable on one side of the equation. Step 4: Solve for $x$.

Let's start solving the equation:

Step 1: Distribute the fractions To distribute the fractions, multiply each term by its respective denominator to eliminate the fractions. For $\frac{5}{6}(x+3)$, we multiply by the common denominator of 6, and for $\frac{1}{4}(x-1)$, we multiply by the common denominator of 4:

$\frac{5}{6}(x+3) + \frac{1}{4}(x-1) = 12$ $\Rightarrow \frac{5}{6} \cdot 6(x+3) + \frac{1}{4} \cdot 4(x-1) = 12 \cdot 6$ $\Rightarrow 5(x+3) + \frac{1}{4} (4)(x-1) = 72$ $\Rightarrow 5(x+3) + (x-1) = 72$

Step 2: Combine like terms Now, simplify the equation by combining like terms:

$5x + 15 + x - 1 = 72$

Step 3: Isolate the variable on one side of the equation To isolate $x$, combine the $x$ terms and move constants to the other side:

$5x + x + 15 - 1 = 72$ $6x + 14 = 72$

Step 4: Solve for $x$ Now, solve for $x$ by subtracting 14 from both sides and then dividing both sides by 6:

$6x = 72 - 14$ $6x = 58$ $x = \frac{58}{6}$ $x = 9.67$

Therefore, the solution to the equation is $x = 9.67$ (rounded to two decimal places).