Simplifying and Combining Like Terms: One sided equations

To solve the equation $2a + 3a + 45a = 0$, follow these steps:

• Step 1: Combine Like Terms.

Add the coefficients of $a$:

$2 + 3 + 45 = 50$

• Step 2: Substitute and Simplify.

This simplifies the equation to:

$50a = 0$

• Step 3: Solve for $a$.

To find $a$, divide both sides of the equation by 50:

$a = \frac{0}{50}$

$a = 0$

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

To solve this problem, we'll proceed with the following steps:

• Step 1: Combine like terms of the given equation.
• Step 2: Solve for the variable $m$.

Now, let's work through these steps:

Step 1: Combine like terms:
We start with the equation $7m + 3m - 40m = 0$.
Combining these like terms entails adding or subtracting the coefficients of $m$:

$(7 + 3 - 40)m = 0$
Calculate the sum and difference of these coefficients:
$(10 - 40)m = 0$

This simplifies to:
$-30m = 0$

Step 2: Solve for $m$:
To isolate $m$, divide both sides by $-30$:
$m = \frac{0}{-30}$

Calculate the right-hand side:

$m = 0$

Therefore, the solution to the problem is $m = 0$. This corresponds to choice 3 from the provided answer options.

Let's combine all the x terms together:

$7x+4x+5x=11x+5x=16x$

The resulting equation is:

$16x=0$

Now let's divide both sides by 16:

$\frac{16x}{16}=\frac{0}{16}$

$x=\frac{0}{16}=0$

To solve the linear equation $a + 7 + 3a - 15 = 0$, we follow these steps:

• Step 1: Combine like terms.
• Step 2: Simplify the equation.
• Step 3: Solve for $a$.

Let's execute each step:

Step 1: Combine like terms.
We have $1a + 3a = 4a$. The equation becomes:

$4a + 7 - 15 = 0$

Step 2: Simplify the equation.
Combine the constants $7$ and $-15$:

$4a - 8 = 0$

Step 3: Solve for $a$.
Add 8 to both sides to isolate the term with $a$:

$4a = 8$

Divide both sides by 4 to solve for $a$:

$a = \frac{8}{4} = 2$

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

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

• Step 1: Simplify the equation by combining like terms.
• Step 2: Isolate the variable $b$ on one side of the equation.
• Step 3: Solve for the value of $b$.

Now, let's work through these steps:
Step 1: Combine the terms $b$ and $2b$ to simplify the equation:
$b + 2b + 4 = 0$ becomes $3b + 4 = 0$.

Step 2: Isolate the variable $b$ by subtracting 4 from both sides:
$3b + 4 - 4 = 0 - 4$ simplifies to $3b = -4$.

Step 3: Solve for $b$ by dividing both sides by 3:
$b = \frac{-4}{3}$.

The solution to the problem is $b = -1\frac{1}{3}$.

Therefore, choice 4 is the correct option: $-1\frac{1}{3}$.

To solve the linear equation $x + 8 + 3x - 4 = 0$, follow these steps:

• Step 1: Combine like terms.
  Combine the terms involving $x$, specifically $x + 3x = 4x$.
  Combine the constant terms, specifically $8 - 4 = 4$.
  The equation becomes $4x + 4 = 0$.
• Step 2: Isolate the variable $x$.
  Subtract 4 from both sides to get $4x = -4$.
• Step 3: Solve for $x$.
  Divide both sides by 4 to solve for $x$, resulting in $x = -1$.

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

Let's solve the equation step by step:

• First, we identify the terms in the equation: $5$, $3$, $x$, $2x$, and $1$.
• Combine like terms on the left side of the equation:
• The constant terms: $5 + 3 + 1 = 9$.
• The terms with $x$: $x + 2x = 3x$.
• Substitute back into the equation to get $9 + 3x = 0$.
• Isolate the term containing $x$ by subtracting 9 from both sides: $3x = -9$.
• Solve for $x$ by dividing both sides by 3: $x = \frac{-9}{3}$.
• Simplify the fraction: $x = -3$.

Therefore, the solution to the equation is $x = -3$.

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

• Step 1: Combine all like terms in the equation.
• Step 2: Simplify to find the value of $x$.

Now, let's work through each step:
Step 1: The equation is $70x + 30x + 10 + 1 + 10x = 0$. We start by combining the like terms:
$70x + 30x + 10x = 110x$.
Thus, the equation simplifies to $110x + 10 + 1 = 0$.

Step 2: Combine the constant terms:
$10 + 1 = 11$.
So, the equation becomes $110x + 11 = 0$.
Subtract 11 from both sides to isolate the term with $x$:
$110x = -11$.

To solve for $x$, divide both sides by 110:
$x = -\frac{11}{110}$.

Simplify the fraction:
$x = -\frac{1}{10}$.

Therefore, the solution to the equation is $x = -\frac{1}{10}$.