Solving Equations Using the Distributive Property

Let's first expand the parentheses using the formula:

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

$(2\times x)+(2\times4)+8=0$

$2x+8+8=0$

Next, we will substitute in our terms accordingly:

$2x+16=0$

Then, we will move the 16 to the left-hand side, keeping the appropriate sign:

$2x=-16$

Finally, we divide both sides by 2:

$\frac{2x}{2}=-\frac{16}{2}$

$x=-8$

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 $-2(-4 + y) - y = 0$, we will follow these steps:

• Step 1: Distribute $-2$ inside the parenthesis.
• Step 2: Simplify and combine like terms.
• Step 3: Solve the equation for $y$.

Let's proceed with the solution:

Step 1: Distribute $-2$ in the expression $-2(-4 + y)$. This will transform the expression as follows:

$-2(-4 + y) = -2 \times -4 + (-2) \times y = 8 - 2y$.

After distributing, the equation becomes:

$8 - 2y - y = 0$.

Step 2: Combine like terms. Notice that $-2y - y$ is equivalent to $-3y$:

$8 - 3y = 0$.

Step 3: Solve for $y$. First, isolate the term with $y$ by subtracting 8 from both sides:

$-3y = -8$.

Next, divide both sides by $-3$ to find $y$:

$y = \frac{-8}{-3} = \frac{8}{3}$.

Thus, the solution for $y$ is $\frac{8}{3}$, which can be written as a mixed number:

$y = 2\frac{2}{3}$.

Therefore, the solution to the problem is $y = 2\frac{2}{3}$.

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

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

$x=-3$