Solve the Linear Equation: 5x-4·3+4x+3x=0

Q: Why do I need to calculate 4 × 3 before combining the x terms?

Because of the order of operations (PEMDAS)! Multiplication must be done before addition or subtraction. If you skip this step, you'll get the wrong constant term and solve the wrong equation.

Q: How do I know which terms are 'like terms'?

Like terms have the same variable and exponent. In this problem, $ 5x $, $ 4x $, and $ 3x $ are all like terms because they all have x to the first power.

Q: Can I rearrange the equation before solving it?

Yes! You can rearrange terms, but always follow order of operations first. Calculate $ 4 \cdot 3 = 12 $, then you can write it as $ 5x + 4x + 3x - 12 = 0 $ if that helps you see the like terms better.

Q: Why is the answer x = 1 and not one of the other choices?

Let's verify: $ 5(1) - 4 \cdot 3 + 4(1) + 3(1) = 5 - 12 + 4 + 3 = 0 $ ✓. The other choices like $ x = 0 $ give $ 0 - 12 + 0 + 0 = -12 \neq 0 $.

Linear Equations with Order of Operations

$5x-4\cdot3+4x+3x=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Always solve multiplication and division before addition and subtraction

00:18 Group terms

00:22 We want to isolate the unknown X

00:25 Arrange the equation so that one side has only the unknown X

00:33 Isolate the unknown X, and calculate

00:45 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

$5x-4\cdot3+4x+3x=0$

Step-by-step solution

To solve this linear equation $5x - 4 \cdot 3 + 4x + 3x = 0$ , follow these steps:

Simplify the expression: First, calculate the product $4 \cdot 3$ . This equals $12$ .
Substitute back into the equation: $5x - 12 + 4x + 3x = 0$ .
Combine like terms:
- The terms involving $x$ are $5x$ , $4x$ , and $3x$ . Add these together: $5x + 4x + 3x = 12x$ .
The equation now simplifies to $12x - 12 = 0$ .
Isolate $x$ : Add $12$ to both sides of the equation to eliminate the constant term on the left:
- $12x - 12 + 12 = 0 + 12$ , which simplifies to $12x = 12$ .
Solve for $x$ : Divide both sides by $12$ to solve for $x$ :
- $x = \frac{12}{12} = 1$ .

The solution to the equation is $x = 1$ .

Verify with the given choices, we find that the correct answer is: $x = 1$ .

Final Answer

$x=1$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Calculate multiplication before addition or subtraction
Technique: Combine like terms: $5x + 4x + 3x = 12x$
Check: Substitute back: $5(1) - 12 + 4(1) + 3(1) = 0$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations
Don't combine x terms before calculating $4 \cdot 3 = 12$ = wrong constant term! This leads to incorrect equations like $12x - 4 \cdot 3 = 0$ instead of $12x - 12 = 0$ . Always follow PEMDAS and multiply first.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ x - 3 + 5 = 8 - 2 $$

FAQ

Everything you need to know about this question

Why do I need to calculate 4 × 3 before combining the x terms?

Because of the order of operations (PEMDAS)! Multiplication must be done before addition or subtraction. If you skip this step, you'll get the wrong constant term and solve the wrong equation.

How do I know which terms are 'like terms'?

Like terms have the same variable and exponent. In this problem, $5x$ , $4x$ , and $3x$ are all like terms because they all have x to the first power.

What if I get a different answer when I check my work?

If your answer doesn't work when you substitute it back, check these steps: (1) Did you calculate $4 \times 3 = 12$ correctly? (2) Did you combine like terms to get $12x$ ? (3) Did you isolate x properly?

Can I rearrange the equation before solving it?

Yes! You can rearrange terms, but always follow order of operations first. Calculate $4 \cdot 3 = 12$ , then you can write it as $5x + 4x + 3x - 12 = 0$ if that helps you see the like terms better.

Why is the answer x = 1 and not one of the other choices?

Let's verify: $5(1) - 4 \cdot 3 + 4(1) + 3(1) = 5 - 12 + 4 + 3 = 0$ ✓. The other choices like $x = 0$ give $0 - 12 + 0 + 0 = -12 \neq 0$ .

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Solve the Linear Equation: 5x-4·3+4x+3x=0

Linear Equations with Order of Operations

❤️ 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 I need to calculate 4 × 3 before combining the x terms?

How do I know which terms are 'like terms'?

What if I get a different answer when I check my work?

Can I rearrange the equation before solving it?

Why is the answer x = 1 and not one of the other choices?

🌟 Unlock Your Math Potential

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