Solving Equations Using All Methods - Examples, Exercises and Solutions

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 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

We open the parentheses according to the formula:

$a(x+b)=ax+ab$

$5\times x+5\times3=0$

$5x+15=0$

We will move the 15 to the right section and keep the corresponding sign:

$5x=-15$

Divide both sections by 5

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

$x=-3$

To solve this equation, follow these steps:

• Step 1: Apply the distributive property to the equation:

  $2(4-x) = 2 \times 4 - 2 \times x = 8 - 2x$

• Step 2: Simplify the equation:

  The equation now becomes: $8 - 2x = 8$

• Step 3: Isolate the variable $x$ by simplifying the equation:

  First, subtract 8 from both sides:
  $8 - 2x - 8 = 8 - 8$
  This simplifies to:
  $-2x = 0$

• Step 4: Solve for $x$ by dividing both sides by -2:

  $x = \frac{0}{-2} = 0$

Therefore, the solution to the equation is $x = 0$.

To open parentheses we will use the formula:

$a(x+b)=ax+ab$

$(7\times-2x)+(7\times5)=77$

We multiply accordingly

$-14x+35=77$

We will move the 35 to the right section and change the sign accordingly:

$-14x=77-35$

We solve the subtraction exercise on the right side and we will obtain:

$-14x=42$

We divide both sections by -14

$\frac{-14x}{-14}=\frac{42}{-14}$

$x=-3$

To solve the equation $x + 3 = 5$, we will follow these steps:

• Subtract 3 from both sides of the equation to isolate $x$.
• On the left, $x + 3 - 3 = x$ remains.
• On the right, $5 - 3 = 2$.
• This gives us the equation: $x = 2$.

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

To solve the equation $3 - x = 1$, we will isolate the variable $x$.

• Step 1: Subtract 3 from both sides of the equation.
  $3 - x - 3 = 1 - 3$

• Step 2: Simplify the expression.
  $-x = -2$

• Step 3: Multiply both sides by $-1$ to solve for $x$.
  $x = 2$

Thus, the solution to the equation is $x = 2$.

To solve the equation $5x = 3$, we will isolate $x$ by using division:

• Step 1: Recognize that $x$ is multiplied by 5. To isolate $x$, we need to undo this multiplication.
• Step 2: Divide both sides of the equation by 5. This step uses the Division Property of Equality:

$\frac{5x}{5} = \frac{3}{5}$

Step 3: Simplify both sides. The left side simplifies to $x$ (because $\frac{5x}{5} = x$), and the right side is $\frac{3}{5}$.

Hence, the solution to the equation $5x = 3$ is $x = \frac{3}{5}$.

We use the formula:

$a\cdot x=b$

$x=\frac{b}{a}$

Note that the coefficient of X is 3.

Therefore, we will divide both sides by 3:

$\frac{3x}{3}=\frac{18}{3}$

Then divide accordingly:

$x=6$

To solve the equation $6x = 3$, follow these steps:

Step 1: We aim to isolate $x$. Divide both sides of the equation by 6 to remove the coefficient attached to $x$:

Step 2: Simplify the fraction on the right side:

Therefore, the solution to the equation $6x = 3$ is $x = \frac{1}{2}$.

To solve the equation $8x = 5$, follow these steps:

• Step 1: Identify the equation $8x = 5$, where $x$ is the unknown variable.
• Step 2: To isolate $x$, divide both sides of the equation by 8.
  This step involves equivalent operations to maintain equality.
• Step 3: Perform the division on both sides:
  $\frac{8x}{8} = \frac{5}{8}$.
  This simplifies to $x = \frac{5}{8}$.

Now, let's outline these steps in detail:

We begin with the equation $8x = 5$.

Dividing both sides by the coefficient of $x$, which is 8, gives:

$\frac{8x}{8} = \frac{5}{8}$.

This simplifies directly to:

$x = \frac{5}{8}$.

Therefore, the solution to the problem is $x = \frac{5}{8}$.

To solve the equation $7x = 4$, we will follow these steps:

• Step 1: We start with the equation $7x = 4$.

• Step 2: Our goal is to isolate $x$. Since $x$ is multiplied by 7, we will divide both sides of the equation by 7.

• Step 3: Performing division: $x = \frac{4}{7}$

Therefore, the solution to the equation $7x = 4$ is $x = \frac{4}{7}$.

We use the formula:

$a\cdot x=b$

$x=\frac{b}{a}$

We multiply the numerator by X and write the exercise as follows:

$\frac{x}{4}=3$

We multiply by 4 to get rid of the fraction's denominator:

$4\times\frac{x}{4}=3\times4$

Then, we remove the common factor from the left side and perform the multiplication on right side to obtain:

$x=12$

To solve the equation $5x = 0$ for $x$, we will use the following steps:

• Step 1: Identify that the equation is $5x = 0$.
• Step 2: To solve for $x$, divide both sides of the equation by 5.

Let's perform the calculation as outlined in Step 2:

$5x = 0$

Divide both sides by 5 to isolate $x$:

Simplifying, this gives:

$x = 0$

Therefore, the solution to the equation $5x = 0$ is $x = 0$.

The correct answer is option 4: $x = 0$.

To solve the equation $4x = \frac{1}{8}$, we need to isolate $x$. We do this by dividing both sides of the equation by the coefficient of $x$, which is 4:

• Step 1: Write the original equation: $4x = \frac{1}{8}$.
• Step 2: Divide both sides by 4 to solve for $x$:

$x = \frac{\frac{1}{8}}{4}$

• Step 3: Simplify the right-hand side by multiplying fractions, recalling that dividing by a number is equivalent to multiplying by its reciprocal:

$x = \frac{1}{8} \times \frac{1}{4} = \frac{1 \times 1}{8 \times 4} = \frac{1}{32}$

Thus, the solution to the equation is $x = \frac{1}{32}$.