All Operations in the Order of Operations: Using variables

We start by substituting the value of $X$

$(4+4)(3+4)$

First, we perform the calculation in parentheses

$(8)(7)$

After this, we solve the parentheses and can continue with the simple multiplication exercise.

$7\times 8=56$

We begin by placing parentheses around the two multiplication exercises:

$(20\times y)+(8\times2)-7=14$

We then solve the exercises within the parentheses:

$20y+16-7=14$

We simplify:

$20y+9=14$

We move the sections:

$20y=14-9$

$20y=5$

We divide by 20:

$y=\frac{5}{20}$

$y=\frac{5}{5\times4}$

We simplify:

$y=\frac{1}{4}$

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:

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

$x=11$

We begin by placing the multiplication exercise inside of parentheses:

$-25-42\colon x+(18\times2)\colon4=-23$

$-25-42\colon x+36\colon4=-23$

We will then place the division exercise inside of parentheses:

$-25-42\colon x+(36\colon4)=-23$

$-25-42\colon x+9=-23$

Next we rearrange the exercise in order to simplify it:

$-25+9-42\colon x=-23$

$(-25+9)-42\colon x=-23$

We then solve the exercise inside of the parenthesis and obtain the following:

$-16-42\colon x=-23$

We rearrange the fractions and obtain the following:

$-42\colon x=-23+16$

$-42\colon x=-7$

We multiply by x and obtain the following:

$-42=-7x$

Lastly we divide by negative 7:

$x=\frac{-42}{-7}=6$

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:

$y=7\times7=49$

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 $5$.