Solve (9+17x)×(6+1)=420: Find the Value of X

Q: Why do I need to solve (6+1) first?

The order of operations (PEMDAS) says parentheses come first! You must calculate $ 6+1=7 $ before multiplying by the other expression.

Q: Can I distribute the multiplication before simplifying the parentheses?

Technically yes, but it's much harder! You'd have to distribute $ (9+17x) $ to both 6 and 1 separately. It's easier to simplify $ (6+1)=7 $ first.

Q: How do I know when to move terms to the other side?

Move terms to isolate the variable! When you have $ 63+119x=420 $, subtract 63 from both sides to get $ 119x=357 $.

Q: How can I check if x = 3 is correct?

Substitute back into the original equation: $ (9+17 \times 3) \times (6+1) = (9+51) \times 7 = 60 \times 7 = 420 $ ✓

Linear Equations with Order of Operations

$(9+17x)\times(6+1)=420$

Calculate a X

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Make sure to open parentheses properly

00:07 Each term in parentheses multiplies each term in the second parentheses

00:25 Solve each multiplication and then sum

00:50 Collect like terms

01:00 Isolate X

01:31 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

$(9+17x)\times(6+1)=420$

Calculate a X

Step-by-step solution

We begin by solving the addition exercise in the right parenthesis:

$(9+17x)\times7=420$

We then multiply each of the terms inside the parentheses by 7:

$(9\times7)+(17x\times7)=420$

We continue by solving each of the exercises inside of the parentheses:

$63+119x=420$

Following this we rearrange the sections whilst maintaining the appropriate sign:

$119x=420-63$

$119x=357$

Finally we divide the two parts by 119:

$\frac{119}{119}x=\frac{357}{119}$

$x=3$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Simplify parentheses first, then multiply or divide
Distribution: Multiply 7 by each term: $7 \times 9 = 63$ and $7 \times 17x = 119x$
Verification: Check by substituting x = 3: $(9+51) \times 7 = 60 \times 7 = 420$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations
Don't solve the multiplication first and ignore the addition in parentheses = wrong setup! This breaks the fundamental rule that parentheses come before multiplication. Always simplify what's inside parentheses first, then multiply.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why do I need to solve (6+1) first?

The order of operations (PEMDAS) says parentheses come first! You must calculate $6+1=7$ before multiplying by the other expression.

Can I distribute the multiplication before simplifying the parentheses?

Technically yes, but it's much harder! You'd have to distribute $(9+17x)$ to both 6 and 1 separately. It's easier to simplify $(6+1)=7$ first.

How do I know when to move terms to the other side?

Move terms to isolate the variable! When you have $63+119x=420$ , subtract 63 from both sides to get $119x=357$ .

What if I get a decimal answer instead of 3?

Check your arithmetic! Common errors include forgetting to simplify $(6+1)$ or making calculation mistakes with $420-63=357$ or $357÷119=3$ .

How can I check if x = 3 is correct?

Substitute back into the original equation: $(9+17 \times 3) \times (6+1) = (9+51) \times 7 = 60 \times 7 = 420$ ✓

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Solve (9+17x)×(6+1)=420: Find the Value of X

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 solve (6+1) first?

Can I distribute the multiplication before simplifying the parentheses?

How do I know when to move terms to the other side?

What if I get a decimal answer instead of 3?

How can I check if x = 3 is correct?

🌟 Unlock Your Math Potential

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