Solving an Equation by Multiplication/ Division: Using order of arithmetic operations

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 linear equation, we'll take the following steps:

• Step 1: Multiply both sides of the equation by 2 to eliminate the fraction.
• Step 2: Simplify and isolate the term containing $x$.
• Step 3: Solve for $x$ by further isolation.

Let's execute these steps:

Step 1: Start with the given equation:

$\frac{-5 + 7x}{2} = 22$

Multiply both sides by 2 to remove the fraction:

$-5 + 7x = 44$

Step 2: Now, eliminate the constant term on the left side by adding 5 to both sides:

$-5 + 7x + 5 = 44 + 5$

This simplifies to:

$7x = 49$

Step 3: Finally, solve for $x$ by dividing both sides by 7:

$x = \frac{49}{7}$

Calculate the result:

$x = 7$

Therefore, the value of $x$ is $x = 7$.

To solve this linear equation $5x - 4 \cdot 3 + 4x + 3x = 0$, follow these steps:

• Simplify the expression: First, calculate the product $4 \cdot 3$. This equals $12$.

• Substitute back into the equation: $5x - 12 + 4x + 3x = 0$.

• Combine like terms:

  • The terms involving $x$ are $5x$, $4x$, and $3x$. Add these together: $5x + 4x + 3x = 12x$.

• The equation now simplifies to $12x - 12 = 0$.

• Isolate $x$: Add $12$ to both sides of the equation to eliminate the constant term on the left:

  • $12x - 12 + 12 = 0 + 12$, which simplifies to $12x = 12$.

• Solve for $x$: Divide both sides by $12$ to solve for $x$:

  • $x = \frac{12}{12} = 1$.

The solution to the equation is $x = 1$.

Verify with the given choices, we find that the correct answer is: $x = 1$.

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

• Step 1: Eliminate multiplication by distributing $2x \cdot 4$.
• Step 2: Combine like terms on the left side of the equation.
• Step 3: Isolate the variable $x$ by moving constants to the opposite side.

Let's work through these steps:

Step 1: The given equation is $2x \cdot 4 - 1 + x + 2 = 19$.
Distribute the multiplication on $2x \cdot 4$ to get $8x$:

$8x - 1 + x + 2 = 19$

Step 2: Combine the like terms ($8x$ and $x$):

$9x - 1 + 2 = 19$

Simplify further by combining constants $-1 + 2$ to get:

$9x + 1 = 19$

Step 3: Isolate $x$ by subtracting 1 from both sides:

$9x = 18$

Finally, divide both sides by 9 to solve for $x$:

$x = \frac{18}{9} = 2$

Therefore, the solution to the problem is $x = 2$.

To solve this problem, we'll proceed with these steps:

• Simplify the equation by performing arithmetic operations.
• Combine like terms.
• Solve the resulting equation for the variable $x$.

Now, let's work through these steps:

Simplify the equation given by performing the multiplication and subtraction:

$5 + 4x - 2 \cdot 3 + 2x \cdot 3 = 9$
$5 + 4x - 6 + 6x = 9$

Combine like terms on the left side:

$(5 - 6) + 4x + 6x = 9$
$-1 + 10x = 9$

To isolate $10x$, add 1 to both sides of the equation:

$10x = 9 + 1$
$10x = 10$

Divide both sides by 10 to solve for $x$:

$x = \frac{10}{10}$
$x = 1$

Therefore, the solution to the equation is $x = 1$.

Comparing this with the provided answer choices, we see that the correct choice is:

$x=1$

To solve the equation $\frac{x+2}{3}=\frac{4}{5}$, we can follow the method of cross-multiplication:

• Step 1: Cross-multiply to eliminate the fractions, giving us:

$(x + 2) \cdot 5 = 4 \cdot 3$

• Step 2: Simplify both sides of the equation:

$5(x + 2) = 12$

• Step 3: Distribute the 5 on the left side:

$5x + 10 = 12$

• Step 4: Subtract 10 from both sides to isolate the term with $x$:

$5x = 2$

• Step 5: Divide both sides by 5 to solve for $x$:

$x = \frac{2}{5}$

Therefore, the solution to the equation is $\frac{2}{5}$.

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 the equation $\frac{x-4}{18} = \frac{7}{9}$, we'll follow these steps:

• Step 1: Apply the principle of cross-multiplication to eliminate fractions.

• Step 2: Solve for the linear expression in terms of $x$.

• Step 3: Isolate $x$ and solve the equation completely.

Now, let's work through each step:
Step 1: Cross-multiply to eliminate the fractions. The equation becomes:

$(x-4) \cdot 9 = 18 \cdot 7 \\ 9(x-4) = 126$

Step 2: Distribute the 9 on the left-hand side:

$9x - 36 = 126$

Step 3: Add 36 to both sides to isolate the term with $x$:

$9x = 126 + 36 9x = 162$

Step 4: Divide both sides by 9 to solve for $x$:

$x = \frac{162}{9} \\ x = 18$

Therefore, the solution to the equation is $x = 18$.

To solve the linear equation $6x \cdot 2 - 4 + 2x + 2 = 5$, follow these steps:

• Step 1: Simplify the expression on the left-hand side of the equation.
• Step 2: Combine like terms to reduce the equation.
• Step 3: Isolate the variable $x$ to determine its value.

Let's simplify and solve the given equation:

Step 1: Simplify the expression $6x \cdot 2 - 4 + 2x + 2$.
This becomes $12x - 4 + 2x + 2$.

Step 2: Combine like terms.
Combine the terms involving $x$: $12x + 2x = 14x$.
Combine the constants: $-4 + 2 = -2$.
This results in the equation $14x - 2 = 5$.

Step 3: Isolate $x$.
Add 2 to both sides to eliminate the constant on the left:
$14x - 2 + 2 = 5 + 2$.
This simplifies to $14x = 7$.
Next, divide both sides by 14 to solve for $x$:
$x = \frac{7}{14}$.

Simplify the fraction:$x = \frac{1}{2}$.

Therefore, the solution to the equation is $x = \frac{1}{2}$.

First, we cross multiply:

$8\times(x+4)=3\times7$

We multiply the right section and expand the parenthesis, multiplying each of the terms by 8:

$8x+32=21$

We rearrange the equation remembering change the plus and minus signs accordingly:

$8x=21-32$
Solve the subtraction exercise on the right side and divide by 8:

$8x=-11$

$\frac{8x}{8}=-\frac{11}{8}$

Convert the simple fraction into a mixed fraction:

$x=-1\frac{3}{8}$