Solve the Linear Equation: a + 7 + 3a - 15 = 0

Q: What are like terms and how do I identify them?

Like terms have the same variable with the same exponent. In this equation, a and 3a are like terms because they both have variable 'a'. Constants like 7 and -15 are also like terms.

Q: Why do I need to combine like terms first?

Combining like terms simplifies the equation and reduces errors. It's much easier to solve $ 4a - 8 = 0 $ than the original messy equation!

Q: What if I forget the negative sign when combining constants?

Be very careful with signs! Remember that $ 7 + (-15) = 7 - 15 = -8 $. Write out each step clearly to avoid sign errors.

Q: How do I check if a = 2 is really correct?

Substitute back: $ 2 + 7 + 3(2) - 15 = 2 + 7 + 6 - 15 = 15 - 15 = 0 $ ✓. Since we get 0, our answer is correct!

Q: Can I solve this equation in a different order?

Yes, but combining like terms first is the most efficient method. You could move terms around, but you'll still need to combine them eventually to get the simplest form.

Linear Equations with Like Term Combination

$a+7+3a-15=0$

$a=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find A

00:03 Collect terms

00:10 Arrange the equation so that one side has only the unknown A

00:20 Isolate A

00:28 This is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$a+7+3a-15=0$

$a=\text{?}$

Step-by-step solution

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 $a = 2$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Combine Like Terms: Group terms with same variable: a + 3a = 4a
Simplify Constants: Calculate 7 - 15 = -8 to get 4a - 8 = 0
Verify Solution: Substitute a = 2: 2 + 7 + 3(2) - 15 = 0 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms first
Don't try to isolate variables without combining like terms = messy equations with multiple variable terms! This makes solving much harder and leads to calculation errors. Always combine all like terms (both variables and constants) before isolating the variable.

Practice Quiz

Test your knowledge with interactive questions

Solve for $$ b $$ :

$$ 8-b=6 $$

FAQ

Everything you need to know about this question

What are like terms and how do I identify them?

Like terms have the same variable with the same exponent. In this equation, a and 3a are like terms because they both have variable 'a'. Constants like 7 and -15 are also like terms.

Why do I need to combine like terms first?

Combining like terms simplifies the equation and reduces errors. It's much easier to solve $4a - 8 = 0$ than the original messy equation!

What if I forget the negative sign when combining constants?

Be very careful with signs! Remember that $7 + (-15) = 7 - 15 = -8$ . Write out each step clearly to avoid sign errors.

How do I check if a = 2 is really correct?

Substitute back: $2 + 7 + 3(2) - 15 = 2 + 7 + 6 - 15 = 15 - 15 = 0$ ✓. Since we get 0, our answer is correct!

Can I solve this equation in a different order?

Yes, but combining like terms first is the most efficient method. You could move terms around, but you'll still need to combine them eventually to get the simplest form.

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