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

It is possible to use the distributive property to simplify the expression below?

What is its simplified form?

$$ (ab)(c d) $$

$$

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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