Solve Linear Equation: 4a+5-24+a=-2a for Variable a

Q: Why do we combine like terms first instead of moving variables right away?

Combining like terms simplifies the equation before moving terms around. It's much easier to work with $ 5a - 19 = -2a $ than the original messy equation!

Q: How do I convert the improper fraction to a mixed number?

Divide the numerator by the denominator: $ \frac{19}{7} = 19 ÷ 7 = 2 $ remainder $ 5 $, so $ \frac{19}{7} = 2\frac{5}{7} $.

Q: How can I check if my mixed number answer is correct?

Convert $ 2\frac{5}{7} $ back to improper fraction $ \frac{19}{7} $, then substitute into the original equation. Both sides should equal the same value!

Q: Why did we add 2a to both sides instead of subtracting 5a?

Both approaches work! Adding $ 2a $ gives us $ 7a = 19 $ (positive coefficient). Subtracting $ 5a $ gives $ -19 = -7a $, then divide by $ -7 $. Choose whichever feels easier!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Collect terms

00:13 Isolate the unknown A

00:37 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

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

$a=?$

2

Step-by-step solution

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: $2\frac{5}{7}$ .

3

Final Answer

$2\frac{5}{7}$

Key Points to Remember

Essential concepts to master this topic

Combine Like Terms: Group all variables together and all constants together
Technique: Move all a terms to one side: 5a + 2a = 7a
Check: Substitute $a = 2\frac{5}{7}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Adding constant to the wrong side when isolating variables
Don't add 19 to both sides when you have 5a - 19 = -2a = wrong operations! This creates 5a = -2a + 19 instead of moving the -2a term. Always move the variable terms first, then handle constants.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do we combine like terms first instead of moving variables right away?

+

Combining like terms simplifies the equation before moving terms around. It's much easier to work with $5a - 19 = -2a$ than the original messy equation!

How do I convert the improper fraction to a mixed number?

+

Divide the numerator by the denominator: $\frac{19}{7} = 19 ÷ 7 = 2$ remainder $5$ , so $\frac{19}{7} = 2\frac{5}{7}$ .

What if I get confused about which side to move the variables to?

+

It doesn't matter which side! You can move all variables to the left or all to the right. Just be consistent and move all variable terms to the same side.

How can I check if my mixed number answer is correct?

+

Convert $2\frac{5}{7}$ back to improper fraction $\frac{19}{7}$ , then substitute into the original equation. Both sides should equal the same value!

Why did we add 2a to both sides instead of subtracting 5a?

+

Both approaches work! Adding $2a$ gives us $7a = 19$ (positive coefficient). Subtracting $5a$ gives $-19 = -7a$ , then divide by $-7$ . Choose whichever feels easier!

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Solve Linear Equation: 4a+5-24+a=-2a for Variable a

Linear Equations with Mixed Number Solutions

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Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do we combine like terms first instead of moving variables right away?

How do I convert the improper fraction to a mixed number?

What if I get confused about which side to move the variables to?

How can I check if my mixed number answer is correct?

Why did we add 2a to both sides instead of subtracting 5a?

🌟 Unlock Your Math Potential

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