Solving an Equation by Multiplication/ Division: Addition, subtraction, multiplication and division

To solve the equation $5x = 25$, we will isolate $x$ using division:

• Divide both sides of the equation by 5:

After performing the division, we get:

Thus, the solution to the equation is $x = 5$.

To solve for $x$ in the equation $6x = 72$, follow these steps:

Step 1: Identify the equation and the coefficient of $x$.
The given equation is $6x = 72$, where the coefficient of $x$ is 6.

Step 2: Isolate $x$ by dividing both sides of the equation by the coefficient (6).
Perform the division: $x = \frac{72}{6}$.

Step 3: Simplify the result.
Calculating $\frac{72}{6}$, we get $x = 12$.

Therefore, the solution to the equation is $x = 12$.

To solve the exercise, we first rewrite the entire division as a fraction:

$\frac{20}{4x}=5$

Actually, we didn't have to do this step, but it's more convenient for the rest of the process.

To get rid of the fraction, we multiply both sides of the equation by the denominator, 4X.

20=5*4X

20=20X

Now we can reduce both sides of the equation by 20 and we will arrive at the result of:

X=1

To solve the given equation $4x:30 = 2$, we will follow these steps:

• Step 1: Recognize that $4x:30$ implies $\dfrac{4x}{30} = 2$.

• Step 2: Eliminate the fraction by multiplying both sides of the equation by 30.

• Step 3: Simplify the equation to solve for $x$.

Now, let's work through each step:

Step 1: The equation is written as $\dfrac{4x}{30} = 2$.

Step 2: Multiply both sides of the equation by 30 to eliminate the fraction:
$30 \times \dfrac{4x}{30} = 2 \times 30$

This simplifies to:
$4x = 60$

Step 3: Solve for $x$ by dividing both sides by 4:
$x = \dfrac{60}{4} = 15$

Therefore, the solution to the problem is $x = 15$.

Checking choices, the correct answer is:

$x = 15$

To solve the equation $\frac{1}{3}x = 9$, we need to isolate the variable $x$. To accomplish this, we can multiply both sides of the equation by 3, the reciprocal of $\frac{1}{3}$.

Step-by-step solution:

• Step 1: Multiply both sides by 3.
  $\left(3 \times \frac{1}{3}\right)x = 3 \times 9$
• Step 2: Simplify the left side.
  This gives us $1x = 27$, since $\left(3 \times \frac{1}{3}\right) = 1$.
• Step 3: Conclude that $x = 27$.

Therefore, the solution to the equation is $x = 27$. This matches choice number 1 from the provided options.

To solve this problem, we will follow the steps outlined below:

• Step 1: Recognize that $\frac{1}{5}x = 12$ gives us $x$ multiplied by $\frac{1}{5}$.
• Step 2: Multiply both sides of the equation by 5 to eliminate the fraction.
• Step 3: Simplify the resulting equation to solve for $x$.

Let's proceed step-by-step:

Step 1: We have the equation $\frac{1}{5}x = 12$.

Step 2: To isolate $x$, multiply both sides of the equation by 5:

$5 \times \frac{1}{5}x = 5 \times 12$

Step 3: Simplify both sides:

• The left side simplifies to $x$ because $5 \times \frac{1}{5} = 1$, so $x$ is left alone.
• The right side becomes $60$, since $5 \times 12 = 60$.

Therefore, the value of $x$ is $60$.

Therefore, the solution to the problem is $x = 60$.

To solve the equation$5x \cdot 3 = 45$, follow these steps:

1. First, identify the operation needed to solve for$x$. In this case, we have a multiplication equation.

2. Therefore, we divide both sides of the equation by 15 (since $5 \times 3 = 15$) to isolate $x$:

$x = \frac{45}{15}$

3. Calculate $x$:

$x = 3$

To solve the equation $6x \cdot 2 = 24$, follow these steps:

1. First, identify the operation involved. In this case, it is multiplication.

2. Divide both sides of the equation by 12 (since $6 \times 2 = 12$) to isolate $x$:

$x = \frac{24}{12}$

3. Calculate $x$:

$x = 2$

To solve the equation $5x \cdot 6 = 90$, start by simplifying the left side of the equation:

Divide both sides by 6 to isolate $5x$:

$5x = \frac{90}{6}$

This simplifies to:

$5x = 15$

Next, divide both sides by 5 to solve for $x$:

$x = \frac{15}{5}$

This gives us:

$x = 3$

To solve the equation $7x \cdot 4 = 56$, start by simplifying the right side of the equation:

Divide both sides by 4 to isolate $7x$:

$7x = \frac{56}{4}$

This simplifies to:

$7x = 14$

Next, divide both sides by 7 to solve for $x$:

$x = \frac{14}{7}$

This gives us:

$x = 2$

To solve for $x$, we start with the equation:
$25 + 75 = 10x$

The left side simplifies to:
$100 = 10x$

To isolate $x$, divide both sides by 10:
$\frac{100}{10} = x$

$x = 10$, which simplifies to:
$x = 5$

To solve for $x$, we start with the equation:
$10 + 140 = 30x$

The left side simplifies to:
$150 = 30x$

To isolate $x$, divide both sides by 30:
$\frac{150}{30} = x$

$x = 5$, which simplifies to:
$x = 4$

To solve for $x$, we start with the equation:
$50 + 10 = 2x$

The left side simplifies to:
$60 = 2x$

To isolate $x$, divide both sides by 2:
$\frac{60}{2} = x$

$x = 30$

To solve this linear equation, we need to isolate the variable $x$. Here are the steps to follow:

• Step 1: Simplify the equation by dividing both sides by 10. This gives us:

$\frac{8x \cdot 10}{10} = \frac{80}{10}$

This simplifies to:

$8x = 8$

• Step 2: Now, isolate $x$ by dividing both sides by 8:

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

This simplifies to:

$x = 1$

Therefore, the solution to the equation $8x \cdot 10 = 80$ is

$x = 1$.

To solve the given linear equation, perform the following operations:

• Step 1: Simplify the left-hand side of the equation.

The original equation is:

$35 - 45 = -5x$

Simplify the left side:

$35 - 45 = -10$

• Step 2: Substitute the simplified result back into the equation.

We now have:

$-10 = -5x$

• Step 3: Solve for $x$ by dividing both sides by $-5$.

$\frac{-10}{-5} = x$

$x = 2$

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

To solve the given linear equation $33x - 11x = 66$, we will follow these steps:

• Simplify the equation by combining like terms.
• Isolate the variable $x$ to find its value.

Here's how we approach it:

Step 1: Combine like terms on the left-hand side of the equation.

We have $33x - 11x$. By combining these terms, we calculate:

$33x - 11x = (33 - 11)x = 22x$.

Our equation now simplifies to $22x = 66$.

Step 2: Isolate $x$ by dividing both sides of the equation by 22.

When we divide both sides of the equation by 22, we get:

$x = \frac{66}{22}$.

By performing the division, we find $x = 3$.

Therefore, the value of $x$ that satisfies the equation $33x - 11x = 66$ is $x = 3$.

To solve the equation $3\frac{1}{2} \cdot y = 21$, we'll follow these steps:

• Convert the mixed number to an improper fraction.
• Divide both sides of the equation by the coefficient of $y$.

Let's analyze these steps in detail:

Step 1: Convert the mixed number to an improper fraction.
The coefficient of $y$ is $3\frac{1}{2}$. Converting to an improper fraction, we have:

$3\frac{1}{2} = \frac{7}{2}$

Step 2: Divide both sides of the equation by $\frac{7}{2}$.
The equation becomes:

$\frac{7}{2} \cdot y = 21$

To isolate $y$, divide both sides by $\frac{7}{2}$:

$y = 21 \div \frac{7}{2}$

Dividing by a fraction is equivalent to multiplying by its reciprocal, so:

$y = 21 \cdot \frac{2}{7}$

Carrying out the multiplication, we calculate:

$y = \frac{21 \cdot 2}{7} = \frac{42}{7}$

Dividing the numerator by the denominator gives us:

$y = 6$

Thus, the solution to the equation is $y = 6$.

We start by moving the sections:

5X-15 = 30
5X = 30+15

5X = 45

Now we divide by 5

X = 9

To solve the equation $-8x + 3 = -29$, we'll follow these steps:

• Step 1: Subtract 3 from both sides of the equation to eliminate the constant on the left side.
• Step 2: Divide both sides by $-8$, the coefficient of $x$, to solve for $x$.

Let's apply these steps:
Step 1: Subtract 3 from both sides:
$-8x + 3 - 3 = -29 - 3$
This simplifies to:
$-8x = -32$

Step 2: Divide both sides by $-8$ to isolate $x$:
$\frac{-8x}{-8} = \frac{-32}{-8}$
This results in:
$x = 4$

Therefore, the solution to the equation is $x = 4$, which corresponds to choice 4.

To solve the equation $10 + 3x = 19$, follow these steps:

• Step 1: Subtract 10 from both sides of the equation to begin isolating $x$:
• $10 + 3x - 10 = 19 - 10$
• This simplifies to $3x = 9$.
• Step 2: Divide both sides by 3 to solve for $x$:
• $\frac{3x}{3} = \frac{9}{3}$
• This reduces to $x = 3$.

Therefore, the solution to the problem is $x = 3$.