Solve the Equation: a^4 + 7a - 5 = 2a + a^4 + 3a - (-a)

Q: Why do the $ a^4 $ terms cancel out?

When you have the same term on both sides of an equation, you can subtract it from both sides. Since $ a^4 $ appears on both sides, subtracting it leaves you with a simpler linear equation.

Q: What does -(-a) actually mean?

The double negative -(-a) means "the opposite of negative a" which equals positive a. Think of it as: minus times minus equals plus, so -(-a) = +a.

Q: How do I combine like terms on the right side?

Add all the 'a' terms together: $ 2a + 3a + a = 6a $. Remember that 'a' by itself means $ 1a $, so you're adding 2 + 3 + 1 = 6.

Q: Can I divide by $ a^4 $ like the explanation shows?

Actually, that's incorrect! You should subtract $ a^4 $ from both sides instead. Dividing assumes $ a ≠ 0 $ and can lead to losing solutions.

Q: How can I check if a = 5 is really correct?

Substitute a = 5 into the original equation:Left side: $ 5^4 + 7(5) - 5 = 625 + 35 - 5 = 655 $Right side: $ 2(5) + 5^4 + 3(5) + 5 = 10 + 625 + 15 + 5 = 655 $Since both sides equal 655, a = 5 is correct!

Linear Equations with Variable Elimination

$a^4+7a-5=2a+a^4+3a-(-a)$

$a=?$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:10 Negative times negative is always positive

00:22 Group like terms

00:29 Simplify what we can

00:34 We want to isolate the unknown A

00:40 Let's arrange the equation so that one side has only A

00:51 Convert from negative to positive

00:57 Negative divided by negative is always positive

01:03 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$a^4+7a-5=2a+a^4+3a-(-a)$

$a=?$

Step-by-step solution

First, let's isolate a from the parentheses in the equation on the right side. We'll remember that minus times minus becomes plus, so we get the equation:

$a^4+7a-5=2a+a^4+3a+a$

Let's continue solving the equation on the right side by adding $2a+3a+a=5a+a=6a$

Now the equation we got is:

$a^4+7a-5=6a+a^4$

Let's divide both sides by $a^4$ and we get:

$7a-5=6a$

Now let's move 6a to the left side and the number 5 to the right side, remembering to change the plus and minus signs accordingly.

The equation we got now is:

$7a-6a=5$

Let's solve the subtraction and we get:

$1a=5$

Let's divide both sides by 1 and we find that $a=5$

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Simplify: Handle negative signs carefully: -(-a) becomes +a
Technique: Subtract $a^4$ from both sides: $7a - 5 = 6a$
Check: Substitute a = 5 back: $7(5) - 5 = 6(5)$ gives 30 = 30 ✓

Common Mistakes

Avoid these frequent errors

Incorrectly handling the double negative -(-a)
Don't leave -(-a) as -a = wrong simplification! This creates 5a instead of 6a on the right side, leading to a = -5. Always remember that minus times minus equals plus, so -(-a) = +a.

Practice Quiz

Test your knowledge with interactive questions

Solve for $$ b $$ :

$$ 8-b=6 $$

FAQ

Everything you need to know about this question

Why do the $a^4$ terms cancel out?

When you have the same term on both sides of an equation, you can subtract it from both sides. Since $a^4$ appears on both sides, subtracting it leaves you with a simpler linear equation.

What does -(-a) actually mean?

The double negative -(-a) means "the opposite of negative a" which equals positive a. Think of it as: minus times minus equals plus, so -(-a) = +a.

How do I combine like terms on the right side?

Add all the 'a' terms together: $2a + 3a + a = 6a$ . Remember that 'a' by itself means $1a$ , so you're adding 2 + 3 + 1 = 6.

Can I divide by $a^4$ like the explanation shows?

Actually, that's incorrect! You should subtract $a^4$ from both sides instead. Dividing assumes $a ≠ 0$ and can lead to losing solutions.

How can I check if a = 5 is really correct?

Substitute a = 5 into the original equation:

Left side: $5^4 + 7(5) - 5 = 625 + 35 - 5 = 655$
Right side: $2(5) + 5^4 + 3(5) + 5 = 10 + 625 + 15 + 5 = 655$

Since both sides equal 655, a = 5 is correct!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Equations (One Variable) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Solve the Equation: a^4 + 7a - 5 = 2a + a^4 + 3a - (-a)

Linear Equations with Variable Elimination

❤️ Continue Your Math Journey!

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 the $a^4$ terms cancel out?

What does -(-a) actually mean?

How do I combine like terms on the right side?

Can I divide by $a^4$ like the explanation shows?

How can I check if a = 5 is really correct?

🌟 Unlock Your Math Potential

More Questions

Solving Equations by using Addition/ Subtraction

Solve the Linear Equation: 11 = a - 16

Solve Linear Equation: 2x+4+28-3x=x Step by Step

Solve for X: Finding the Variable in 72-x=63

Solve -3(4a+8)=27a: Linear Equation with Distributive Property

Solving an Equation by Multiplication/ Division

Solve for X: Similar Triangles with Expressions 6X and 10X-58

Solve for X: Triangle with Angles 6X and 7X+5 - Geometric Proof

Solve for b in 2b-3b+4=5: Linear Equation Solution

Solve the Equation: -y/5 = -25 | Linear Equation Practice

Simplifying and Combining Like Terms

Solve the Linear Equation: -16 + a = -17

Solve the Linear Equation: 2b + 16 + b = -2

Solve for b: 4(b/2 + b) - 1/3 = 6b Linear Equation

Solve the Linear Equation: Finding b in 8-b=6

Solve the Equation: a^4 + 7a - 5 = 2a + a^4 + 3a - (-a)

Linear Equations with Variable Elimination

❤️ Continue Your Math Journey!

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 the a4 a^4 a4 terms cancel out?

What does -(-a) actually mean?

How do I combine like terms on the right side?

Can I divide by a4 a^4 a4 like the explanation shows?

How can I check if a = 5 is really correct?

🌟 Unlock Your Math Potential

More Questions

Solving Equations by using Addition/ Subtraction

Solve the Linear Equation: 11 = a - 16

Solve Linear Equation: 2x+4+28-3x=x Step by Step

Solve for X: Finding the Variable in 72-x=63

Solve -3(4a+8)=27a: Linear Equation with Distributive Property

Solving an Equation by Multiplication/ Division

Solve for X: Similar Triangles with Expressions 6X and 10X-58

Solve for X: Triangle with Angles 6X and 7X+5 - Geometric Proof

Solve for b in 2b-3b+4=5: Linear Equation Solution

Solve the Equation: -y/5 = -25 | Linear Equation Practice

Simplifying and Combining Like Terms

Solve the Linear Equation: -16 + a = -17

Solve the Linear Equation: 2b + 16 + b = -2

Solve for b: 4(b/2 + b) - 1/3 = 6b Linear Equation

Solve the Linear Equation: Finding b in 8-b=6

Why do the $a^4$ terms cancel out?

Can I divide by $a^4$ like the explanation shows?