Solving Equations by using Addition/ Subtraction: Solving the problem

First, we solve the multiplication and division exercises, we will put them in parentheses to avoid confusion:

$92-(x\times2)-(24\colon4)=64$

$92-2x-6=64$

Reduce:

$86-2x=64$

Move the sides:

$-2x=64-86$

$-2x=-22$

Divide by negative 2:

$x=\frac{-22}{-2}$

$x=11$

To solve this problem, we'll follow these steps:

• Simplify the term $2y \cdot \frac{1}{y}$
• Rearrange the equation to group similar terms
• Solve for $y$

Now, let's work through each step:

Step 1: Simplify the expression $2y \cdot \frac{1}{y}$.

The term $2y \cdot \frac{1}{y}$ simplifies directly to $2$ since $y$ in the numerator and denominator cancel each other out assuming $y \neq 0$. Therefore, the equation becomes:

$2 - y + 4 = 8y$

Step 2: Combine like terms on the left-hand side:

$2 + 4 = 6$, so the equation now is $6 - y = 8y$.

Step 3: Rearrange the equation to isolate $y$ on one side. Add $y$ to both sides to get rid of the negative $y$:

$6 = 8y + y$

This simplifies to:

$6 = 9y$

Step 4: Solve for $y$ by dividing both sides by 9:

$y = \frac{6}{9}$

Simplify the fraction to get:

$y = \frac{2}{3}$

Therefore, the solution to the problem is $\frac{2}{3}$.

To solve for$x$ in the equation $(32 - 17) \times 4 \times 9 \colon 3 - 50 \colon x = 170$, we will follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

Step 1: Evaluate the Parentheses
First, solve the expression inside the parentheses: $32 - 17 = 15$.

Substitute back into the equation:
$15 \times 4 \times 9 \colon 3 - 50 \colon x = 170$.

Step 2: Perform Multiplication and Division
Continue with the multiplication and division from left to right.

• First, multiply$15$ and $4$:
  $15 \times 4 = 60$

• Next, multiply $60$ by $9$:
  $60 \times 9 = 540$

• Then, divide $540$ by$3$:
  $540 \colon 3 = 180$

• Now, subtract $\frac{50}{x}$ from $180$:
  $180 - \frac{50}{x} = 170$

Step 3: Isolate $x$
We isolate$x$ by adding $\frac{50}{x}$ to both sides of the equation:
$180 = 170 + \frac{50}{x}$

Subtract 170 from both sides:
$180 - 170 = \frac{50}{x}$

This simplifies to:
$10 = \frac{50}{x}$

Step 4: Solve for$x$
To find $x$, solve the equation$10x = 50$ which is derived from multiplying both sides by $x$:
$x = \frac{50}{10}$

The value of $x$ is:
$x = 5$

The final answer is $5$.

We begin by solving the multiplication exercise:

$12\times(-5)=-60$

and subsequently the exercises within brackets:

$21-4=17$

We obtain the following:

$23-(-60)+y:7+17=107$

Keep in mind that a negative times a negative becomes a positive:

$23+60+y:7+17=107$

Next we simplify and add:

$23+60=83$

$83+17=100$

We obtain the following calculation:

$100+y:7=107$

We then rearrange the sections:

$y:7=107-100$

$\frac{y}{7}=7$

Lastly we multiply by 7:

$y=7\times7=49$