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

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 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 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:
$25 + 75 = 10x$

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:
$50 + 10 = 2x$

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

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

$x = 30$

To solve 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 $6x \cdot 2 = 24$, 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 $7x \cdot 4 = 56$, 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:

$x = 2$

We start by moving the sections:

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

5X = 45

Now we divide by 5

X = 9

We have an equation with a variable.

Usually, in these equations, we will be asked to find the value of the missing (X),

This is how we solve it:

To solve the exercise, first we have to change the mixed fractions to an improper fraction,

So that it will then be easier for us to solve them.

Let's start with the four and the third:

To convert a mixed fraction, we start by multiplying the whole number by the denominator

4*3=12

Now we add this to the existing numerator.

12+1=13

And we find that the first fraction is 13/3

Let's continue with the second fraction and do the same in it:
21*3=63

63+2=65

The second fraction is 65/3

We replace the new fractions we found in the equation:

 13/3x = 65/3

At this point, we will notice that all the fractions in the exercise share the same denominator, 3.

Therefore, we can multiply the entire equation by 3.

13x=65

Now we want to isolate the unknown, the x.

Therefore, we divide both sides of the equation by the unknown coefficient -
13.

63:13=5

x=5