Solving an Equation by Multiplication/ Division: One sided equations

Start by simplifying the left-hand side of the equation:

$3x - x = 2x$

So the equation becomes:

$2x = 8$

To find the value of $x$ , divide both sides by 2:

$x = \frac{8}{2}$

Then simplify the fraction:

$x = 4$

Thus, the solution to the equation is$x = 4$.

Combine like terms on the left-hand side:

$4x + 2x = 6x$

The equation becomes:

$6x = 18$

Divide both sides by 6 to solve for $x$ :

$x = \frac{18}{6}$

Simplify the division:

$x = 3$

Thus, $x = 3$ is the solution to the equation.

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

• Combine like terms on the left side of the equation.
• Solve for $x$ by isolating it on one side of the equation.

Let's work through the solution:

Step 1: Combine like terms in the equation $x + 2x = 9$. The terms $x$ and $2x$ are like terms because they both contain the variable $x$. When combined, these terms give us:

$x + 2x = 3x$

Step 2: The equation now simplifies to:

$3x = 9$

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

$x = \frac{9}{3}$

The calculation gives us:

$x = 3$

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

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

• Step 1: Identify the like terms on the left-hand side of the equation.
• Step 2: Combine like terms.
• Step 3: Simplify the equation.
• Step 4: Solve the equation for $b$.

Now, let's work through each step:

Step 1: The given equation is $5b + 300b = 0$.

Step 2: Combine like terms:

$5b + 300b = (5 + 300)b = 305b$

So, the equation becomes $305b = 0$.

Step 3: Since $305b = 0$, we can solve for $b$ using the property of zero product:

If $305 \times b = 0$, then $b$ must be $0$ because $305 \neq 0$.

Therefore, the solution to the problem is $b = 0$.

To solve the equation $3x + 5 = 20$, follow these steps:

1. Subtract 5 from both sides: $3x = 20 - 5$

2. Simplify the right side: $3x = 15$

3. Divide both sides by 3: $x = \frac{15}{3}$

4. Solve: $x = 5$

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 $4a + 5 - 24 + a = -2a$, 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 $2 + 3a + 4 = 0$, 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 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 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 $2y + 12 - 5y + 30 = 0$, follow these steps:

• Step 1: Simplify the equation by combining like terms.
  Combine the $y$ terms and the constant terms:
  $2y - 5y + 12 + 30 = 0$
• Step 2: Calculate the combined terms.
  $2y - 5y = -3y$
  $12 + 30 = 42$
  Thus, the equation becomes:
  $-3y + 42 = 0$
• Step 3: Isolate the variable $y$.
  Subtract 42 from both sides to get:
  $-3y = -42$
• Step 4: Solve for $y$ by dividing both sides by $-3$:
  $y = \frac{-42}{-3}$
• Step 5: Simplify the fraction:
  $y = 14$

Therefore, the solution to the equation is $y = 14$.

Let's first arrange the equation so that on the left-hand side we have the terms with the coefficient $b$ and on the right-hand side the numbers without the coefficient $b$.

Remember that when we move terms across the equals sign, the plus and minus signs will change accordingly:

$2b-3b=5-4$

Let's now solve the subtraction exercise on both sides:

$-1b=1$

Finally, we can divide both sides by -1 to find our answer:

$b=-1$

To solve the equation $\frac{x}{4} + 2x - 18 = 0$, we proceed as follows:

• Step 1: Eliminate the fraction by multiplying the entire equation by 4:
  $(4) \Big(\frac{x}{4} + 2x - 18\Big) = (4)(0)$
• Step 2: Distribute and simplify:
  $x + 8x - 72 = 0$
• Step 3: Combine like terms:
  $9x - 72 = 0$
• Step 4: Isolate $9x$ by adding 72 to both sides:
  $9x = 72$
• Step 5: Solve for $x$ by dividing both sides by 9:
  $x = \frac{72}{9}$
• Step 6: Simplify the division:
  $x = 8$

Thus, the solution to the problem is $x = 8$.

To solve the equation $3x + 4 + 8x - 15 = 0$, we begin by combining the terms that involve $x$ and the constant terms:

Step 1: Combine like terms.
The terms involving $x$ are $3x$ and $8x$. Adding these yields:

The constant terms are $+4$ and $-15$. Combining these gives:

Thus, the equation becomes:

Step 2: Solve for $x$.
To isolate $x$, add 11 to both sides of the equation:

Now, divide both sides by 11:

Therefore, the solution to the equation is $x = 1$.

To solve the equation $12y + 4y + 5 - 3 = 2y$, we'll follow these steps:

• **Step 1**: Simplify the left side of the equation by combining like terms: $12y + 4y = 16y$.
• **Step 2**: Replace that in the equation: $16y + 5 - 3 = 2y$. Simplify further to $16y + 2 = 2y$.
• **Step 3**: Isolate $y$ by getting all the terms involving $y$ on one side. Subtract $2y$ from both sides, yielding: $16y - 2y = -2$.
• **Step 4**: This simplifies to $14y = -2$.
• **Step 5**: Divide each side by 14 to solve for $y$: $y = \frac{-2}{14}$.
• **Step 6**: Simplify the fraction: $y = -\frac{1}{7}$.

Therefore, the solution to the problem is $y = -\frac{1}{7}$.

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

• Simplify the term $2y \cdot \frac{1}{y}$
• Rearrange the equation to group similar terms
• Solve for $y$

Now, let's work through each step:

Step 1: Simplify the expression $2y \cdot \frac{1}{y}$.

The term $2y \cdot \frac{1}{y}$ simplifies directly to $2$ since $y$ in the numerator and denominator cancel each other out assuming $y \neq 0$. Therefore, the equation becomes:

$2 - y + 4 = 8y$

Step 2: Combine like terms on the left-hand side:

$2 + 4 = 6$, so the equation now is $6 - y = 8y$.

Step 3: Rearrange the equation to isolate $y$ on one side. Add $y$ to both sides to get rid of the negative $y$:

$6 = 8y + y$

This simplifies to:

$6 = 9y$

Step 4: Solve for $y$ by dividing both sides by 9:

$y = \frac{6}{9}$

Simplify the fraction to get:

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

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

To solve the given linear equation, we will follow these steps:

• Step 1: Combine the terms involving $y$.
• Step 2: Simplify the constants on the right side of the equation.
• Step 3: Isolate $y$ to find its value.

Let’s solve the equation $\frac{1}{4}y + \frac{1}{2}y + 5 - 12 = 0$.

Step 1: Combine the like terms that involve $y$.
The coefficients of $y$ are $\frac{1}{4}$ and $\frac{1}{2}$. To combine them, we need a common denominator, which is 4. Therefore:

$\frac{1}{4}y + \frac{1}{2}y = \frac{1}{4}y + \frac{2}{4}y = \frac{3}{4}y$.

Step 2: Simplify the constants.
The equation now becomes $\frac{3}{4}y + 5 - 12 = 0$.
Combine the constants: $5 - 12 = -7$.

The equation simplifies to $\frac{3}{4}y - 7 = 0$.

Step 3: Isolate $y$.
Add 7 to both sides of the equation:
$\frac{3}{4}y = 7$.

To solve for $y$, multiply both sides by the reciprocal of $\frac{3}{4}$, which is $\frac{4}{3}$:

$y = 7 \times \frac{4}{3} = \frac{28}{3}$.

Convert the fraction to a mixed number: $\frac{28}{3} = 9 \cdot 3 + 1 = 9 \text{ remainder } 1$. Thus, $\frac{28}{3} = 9\frac{1}{3}$.

Therefore, the value of $y$ is $9\frac{1}{3}$.