Solving an Equation by Multiplication/ Division: Rearranging Equations

Step-by-step solution:

1. Start with the equation: $3x + 6 = 12$

2. Subtract 6 from both sides: $3x + 6 - 6 = 12 - 6$, which simplifies to $3x = 6$

3. Divide both sides by 3 to solve for x: $x = \frac{6}{3}$

4. Simplify the division: $x = 2$

To solve for$x$, first, get all terms involving $x$ on one side and constants on the other. Start from:

$4x - 7 = x + 5$

Subtract $x$ from both sides to simplify:

$3x - 7 = 5$

Add 7 to both sides to isolate the terms with$x$:

$3x = 12$

Divide each side by 3 to solve for$x$:

$x = 4$

Thus, $x$ is $4$.

To solve the equation $5x + 10 = 3x + 18$, follow these steps:

1. Subtract $3x$ from both sides to get:

$5x - 3x + 10 = 18$

2. Simplify the equation:

$2x + 10 = 18$

3. Subtract $10$ from both sides:

$2x = 8$

4. Divide both sides by $2$:

$x = 4$

Step-by-step solution:

1. Begin with the equation: $5x - 3 = 2$

2. Add 3 to both sides: $5x - 3 + 3 = 2 + 3$, which simplifies to $5x = 5$

3. Divide both sides by 5 to solve for x: $x = \frac{5}{5}$

4. Simplify the division: $x = 1$

To solve the equation $7x - 3 = 4x + 9$, follow these steps:

1. Subtract $4x$ from both sides to get:

$7x - 4x - 3 = 9$

2. Simplify the equation:

$3x - 3 = 9$

3. Add $3$ to both sides:

$3x = 12$

4. Divide both sides by $3$:

$x=4$

To solve the equation $4x - 7 = 13$, follow these steps:

1. Add 7 to both sides: $4x = 13 + 7$

2. Simplify the right side: $4x = 20$

3. Divide both sides by 4: $x = \frac{20}{4}$

4. Solve: $x = 5$

To solve the equation $10 + 9x = 91$, we'll follow these steps:

• Step 1: Eliminate the constant term on the left side by subtracting 10 from both sides of the equation.

$10 + 9x - 10 = 91 - 10$ $9x = 81$

• Step 2: Solve for $x$ by dividing each side of the equation by the coefficient of $x$, which is 9.

$\frac{9x}{9} = \frac{81}{9}$ $x = 9$

Hence, the value of $x$ is $9$.

To solve the equation $5x + 6 = 56$, we will follow these steps:

• Step 1: Subtract 6 from both sides of the equation to eliminate the constant term on the left-hand side.
• Step 2: Simplify the resulting equation.
• Step 3: Divide both sides by 5 to isolate $x$.

Now, perform each step:

Step 1: Subtract 6 from both sides:
$5x + 6 - 6 = 56 - 6$

Step 2: Simplify both sides:
$5x = 50$

Step 3: Divide both sides by 5 to solve for $x$:
$x = \frac{50}{5}$

Step 4: Simplify the division:

$x = 10$

Therefore, the solution to the problem is $x = 10$.

To solve the equation $4a + 5 - 24 + a = -2a$, follow these steps:

• Step 1: Start by combining like terms on the left side of the equation:

$4a + a + 5 - 24 = -2a$

This simplifies to:

$5a - 19 = -2a$

• Step 2: Move all terms involving $a$ to one side of the equation and constant terms to the other side:

Add $2a$ to both sides to collect all terms with $a$:

$5a + 2a = 19$

This simplifies to:

$7a = 19$

• Step 3: Solve for $a$ by dividing both sides by 7:

$a = \frac{19}{7}$

Thus, the value of $a$ is $\frac{19}{7}$, which can be written as a mixed number:

$a = 2\frac{5}{7}$.

Upon verifying with the given choices, the correct answer is choice 1: $2\frac{5}{7}$.

To solve the problem, we will use the following steps:

• Step 1: Simplify the equation by combining like terms.
• Step 2: Isolate the variable $m$ using algebraic methods.
• Step 3: Solve for $m$ and verify the solution.

Let's begin:

Step 1: Simplify the equation $m + 3m - 17m + 6 = -20$.
Combine the coefficients of $m$:

$(1 + 3 - 17)m + 6 = -20$

This simplifies to:

$-13m + 6 = -20$

Step 2: Isolate $m$.
Subtract 6 from both sides:

$-13m + 6 - 6 = -20 - 6$

Simplifies to:

$-13m = -26$

Step 3: Solve for $m$ by dividing both sides by -13:

$m = \frac{-26}{-13}$

The division simplifies to:

$m = 2$

Therefore, the solution to the problem is $m = 2$, which corresponds to choice 2 in the given options.

To solve the equation $5x + 4 = 7x$, we will proceed as follows:

• Step 1: Subtract $5x$ from both sides to simplify the equation.

The equation is:
$5x + 4 - 5x = 7x - 5x$

This simplifies to:
$4 = 2x$

• Step 2: To solve for $x$, divide both sides by 2 to isolate $x$.

Perform the division:
$\frac{4}{2} = \frac{2x}{2}$

This gives us:
$2 = x$

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

To solve the equation $2 + 3a + 4 = 0$, follow these steps:

• Step 1: Combine the constant terms on the left side.
  The terms $2$ and $4$ can be combined to get $6$.
  Hence, the equation becomes $3a + 6 = 0$.
• Step 2: Isolate the term with the variable $a$.
  Subtract $6$ from both sides to get $3a = -6$.
• Step 3: Solve for $a$ by dividing both sides by the coefficient of $a$, which is $3$.
  Thus, $a = \frac{-6}{3} = -2$.

Therefore, the solution to the problem is $a = -2$.

To solve this linear equation, follow these steps:

• Step 1: Isolate the term with $x$ by subtracting 7 from both sides of the equation.
• Step 2: Perform the subtraction to simplify the equation.
• Step 3: Divide both sides by 5 to solve for $x$.

Let’s perform each step:

Step 1: Subtract 7 from both sides:
$5x + 7 - 7 = 32 - 7$

This simplifies to:
$5x = 25$

Step 2: Divide both sides by 5 to isolate $x$:
$x = \frac{25}{5}$

Perform the division:
$x = 5$

Hence, the solution to the equation $5x + 7 = 32$ is $x = 5$.

We will solve the given linear equation $8x + 4 = 4$ step-by-step:

Step 1: Subtract 4 from both sides of the equation to begin isolating the variable $x$:

$8x + 4 - 4 = 4 - 4$

This simplifies to:

$8x = 0$

Step 2: Divide both sides of the equation by 8 to solve for $x$:

$\frac{8x}{8} = \frac{0}{8}$

This results in:

$x = 0$

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

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

• Step 1: Subtract 13 from both sides of the equation to isolate the term with $x$.
• Step 2: Divide by $-2$ to solve for $x$.

Now, let's work through each step:
Step 1: Begin by subtracting 13 from both sides:

$13 - 2x - 13 = 0 - 13$
Which simplifies to:

$-2x = -13$

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

$\frac{-2x}{-2} = \frac{-13}{-2}$

This simplifies to:

$x = \frac{13}{2}$

When expressed as a mixed number, $x$ equals:

$x = 6\frac{1}{2}$.

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

The correct answer choice is :

$x = 6\frac{1}{2}$

To solve the equation $14x - 6 = 134$, follow these steps:

• Step 1: Isolate the term involving $x$. We do this by adding 6 to both sides of the equation to eliminate the constant term:

$14x - 6 + 6 = 134 + 6$

This simplifies to:

$14x = 140$

• Step 2: Solve for $x$ by dividing both sides by 14 (the coefficient of $x$):

$\frac{14x}{14} = \frac{140}{14}$

This gives us:

$x = 10$

Therefore, the solution to the problem is $x = 10$.

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

• Step 1: Combine like terms on the left side of the equation.
• Step 2: Isolate the variable $x$ on one side of the equation.
• Step 3: Solve for $x$ and simplify the result.

Now, let's work through each step:
Step 1: The left side of the equation is $800 - 2x - x$. Combine the terms with $x$:
This becomes $800 - 3x = 803$.

Step 2: Subtract 800 from both sides to isolate the term with $x$:
$800 - 3x - 800 = 803 - 800$
This simplifies to $-3x = 3$.

Step 3: Divide both sides by -3 to solve for $x$:
$x = \frac{3}{-3}$
Thus, $x = -1$.

Therefore, the solution to the problem is $x = -1$.

To solve this problem, we need to find $x$ in the equation:

$20 + 20x - 3x = 88$

Step 1: Combine like terms on the left-hand side of the equation. The terms involving $x$ are $20x$ and $-3x$.

$20x - 3x = 17x$

Thus, the equation becomes:

$20 + 17x = 88$

Step 2: Isolate the $x$-related terms by moving the constant term to the right-hand side. To do this, subtract 20 from both sides:

$17x = 88 - 20$

$17x = 68$

Step 3: Solve for $x$ by dividing both sides of the equation by 17:

$x = \frac{68}{17}$

$x = 4$

Therefore, the solution to the problem is $x = 4$.

To solve the equation $-8x + 3 = -29$, we'll follow these steps:

• Step 1: Subtract 3 from both sides of the equation to eliminate the constant on the left side.
• Step 2: Divide both sides by $-8$, the coefficient of $x$, to solve for $x$.

Let's apply these steps:
Step 1: Subtract 3 from both sides:
$-8x + 3 - 3 = -29 - 3$
This simplifies to:
$-8x = -32$

Step 2: Divide both sides by $-8$ to isolate $x$:
$\frac{-8x}{-8} = \frac{-32}{-8}$
This results in:
$x = 4$

Therefore, the solution to the equation is $x = 4$, which corresponds to choice 4.

To solve the equation $10 + 3x = 19$, follow these steps:

• Step 1: Subtract 10 from both sides of the equation to begin isolating $x$:
• $10 + 3x - 10 = 19 - 10$
• This simplifies to $3x = 9$.
• Step 2: Divide both sides by 3 to solve for $x$:
• $\frac{3x}{3} = \frac{9}{3}$
• This reduces to $x = 3$.

Therefore, the solution to the problem is $x = 3$.