Solving Equations Using All Methods: Addition, subtraction, multiplication and division

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 $x$:

$x = \frac{0}{5}$

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 $5x = 1$, we need to isolate $x$. Here are the steps:

• Step 1: Start with the equation $5x = 1$.
• Step 2: Divide both sides of the equation by the coefficient of $x$, which is 5, to isolate $x$. This gives us:
$\frac{5x}{5} = \frac{1}{5}$
• Step 3: Simplify the left side:
$\frac{5x}{5} = x$
• Step 4: Write the simplified equation:
$x = \frac{1}{5}$

Therefore, the solution to the equation $5x = 1$ is $x = \frac{1}{5}$.

The correct answer choice is:

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

To solve the equation $6 - 4x = -18$, we follow these steps:

• Step 1: Subtract 6 from both sides of the equation to begin isolating the term with $x$:

$6 - 4x - 6 = -18 - 6$

This simplifies to:

$-4x = -24$

• Step 2: Divide both sides by -4 to solve for $x$:

$\frac{-4x}{-4} = \frac{-24}{-4}$

The equation simplifies to:

$x = 6$

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

To solve the equation $-8 - x = -5$, we'll isolate the variable $x$ by performing algebraic operations:

Step 1: Add 8 to both sides of the equation to eliminate the $-8$:

$-8 - x + 8 = -5 + 8$

This simplifies to:

$-x = 3$

Step 2: To solve for $x$, we need to change the sign of $x$. Multiply both sides by $-1$:

$x = -3$

Therefore, the solution to the equation is $\boxed{-3}$.