Solving an Equation by Multiplication/ Division: Number of terms

To solve the linear equation $6x \cdot 2 - 4 + 2x + 2 = 5$, follow these steps:

• Step 1: Simplify the expression on the left-hand side of the equation.
• Step 2: Combine like terms to reduce the equation.
• Step 3: Isolate the variable $x$ to determine its value.

Let's simplify and solve the given equation:

Step 1: Simplify the expression $6x \cdot 2 - 4 + 2x + 2$.
This becomes $12x - 4 + 2x + 2$.

Step 2: Combine like terms.
Combine the terms involving $x$: $12x + 2x = 14x$.
Combine the constants: $-4 + 2 = -2$.
This results in the equation $14x - 2 = 5$.

Step 3: Isolate $x$.
Add 2 to both sides to eliminate the constant on the left:
$14x - 2 + 2 = 5 + 2$.
This simplifies to $14x = 7$.
Next, divide both sides by 14 to solve for $x$:
$x = \frac{7}{14}$.

Simplify the fraction:$x = \frac{1}{2}$.

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

To solve this linear equation $5x - 4 \cdot 3 + 4x + 3x = 0$, follow these steps:

• Simplify the expression: First, calculate the product $4 \cdot 3$. This equals $12$.

• Substitute back into the equation: $5x - 12 + 4x + 3x = 0$.

• Combine like terms:

  • The terms involving $x$ are $5x$, $4x$, and $3x$. Add these together: $5x + 4x + 3x = 12x$.

• The equation now simplifies to $12x - 12 = 0$.

• Isolate $x$: Add $12$ to both sides of the equation to eliminate the constant term on the left:

  • $12x - 12 + 12 = 0 + 12$, which simplifies to $12x = 12$.

• Solve for $x$: Divide both sides by $12$ to solve for $x$:

  • $x = \frac{12}{12} = 1$.

The solution to the equation is $x = 1$.

Verify with the given choices, we find that the correct answer is: $x = 1$.

To solve this problem, we'll follow these steps:

• Simplify the equation by combining like terms.
• Isolate $x$ on one side of the equation.
• Solve for $x$.

Now, let's work through each step:
First, simplify the expression on the left side of the equation:

$3 + 4x - 2 \cdot 1 + 4x = 17$

Calculate $2 \cdot 1$, which is $2$. Then, replace that in the equation:

$3 + 4x - 2 + 4x = 17$

Next, combine the constant terms $3$ and $-2$:

$(3 - 2) + 4x + 4x = 17$

This simplifies to:

$1 + 4x + 4x = 17$

Now, combine the $x$-terms:

$1 + 8x = 17$

Isolate the $x$-term by subtracting $1$ from both sides:

$8x = 17 - 1$

This simplifies to:

$8x = 16$

Finally, solve for $x$ by dividing both sides by $8$:

$x = \frac{16}{8}$

Which simplifies to:

$x = 2$

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