Simplifying and Combining Like Terms - Examples, Exercises and Solutions

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 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.

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 the equation $x + x = 8$, follow these steps:

• Step 1: Combine like terms. Since the left side of the equation is $x + x$, it can be simplified to $2x$. This gives us the equation $2x = 8$.
• Step 2: Solve for $x$ by isolating it. Divide both sides of the equation by 2 to get $x$.
• Performing the division gives $x = \frac{8}{2}$.
• Step 3: Calculate the result of the division. $\frac{8}{2} = 4$.

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

Let's solve the equation $-16 + a = -17$ by isolating the variable $a$.

To isolate $a$, add 16 to both sides of the equation to cancel out the $-16$:

$-16 + a + 16 = -17 + 16$

This simplification results in:

$a = -1$

Thus, the solution to the equation $-16 + a = -17$ is $a = -1$.

If we review the answer choices given, the correct answer is Choice 4, $-1$.

The solution to the problem is $a = -1$.