Solve (7x+3)×(10+4)=238: Step-by-Step Linear Equation

Linear Equations with Parentheses Distribution

(7x+3)×(10+4)=238 (7x+3)\times(10+4)=238

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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
00:44 Collect like terms
00:57 Isolate X
01:29 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

(7x+3)×(10+4)=238 (7x+3)\times(10+4)=238

2

Step-by-step solution

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

(7x+3)+14=238 (7x+3)+14=238

We then multiply each of the terms inside of the parentheses by 14:

(14×7x)+(14×3)=238 (14\times7x)+(14\times3)=238

Following this we solve each of the exercises inside of the parentheses:

98x+42=238 98x+42=238

We move the sections whilst retaining the appropriate sign:

98x=23842 98x=238-42

98x=196 98x=196

Finally we divide the two parts by 98:

9898x=19698 \frac{98}{98}x=\frac{196}{98}

x=2 x=2

3

Final Answer

2

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Simplify expressions in parentheses before distributing multiplication
  • Distribution: Multiply (7x+3)×14=98x+42 (7x+3) \times 14 = 98x + 42
  • Check: Substitute x = 2: (7(2)+3)×14=17×14=238 (7(2)+3) \times 14 = 17 \times 14 = 238

Common Mistakes

Avoid these frequent errors
  • Forgetting to simplify parentheses first
    Don't distribute (7x+3) before calculating (10+4) = wrong order of operations! This leads to more complex calculations and potential errors. Always simplify expressions in parentheses first, then distribute.

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 (10+4) first instead of distributing immediately?

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The order of operations (PEMDAS) requires you to simplify what's inside parentheses first. This gives you (7x+3)×14=238 (7x+3) \times 14 = 238 , which is much easier to work with than distributing both 10 and 4 separately.

What does it mean to 'distribute' the 14?

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Distributing means multiplying 14 by each term inside the parentheses: 14×7x=98x 14 \times 7x = 98x and 14×3=42 14 \times 3 = 42 . This gives you 98x+42=238 98x + 42 = 238 .

How do I isolate x after distributing?

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First, subtract 42 from both sides to get 98x=196 98x = 196 . Then divide both sides by 98 to find x=2 x = 2 . Always do the opposite operations to undo what's being done to x.

What if I get a different answer when I check?

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If your check doesn't work, go back and look for these common errors: arithmetic mistakes when distributing, forgetting to subtract 42 from both sides, or division errors. Double-check each step carefully!

Can I solve this equation differently?

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You could expand everything first, but it's much easier to simplify (10+4)=14 (10+4) = 14 first. This reduces the complexity and follows proper order of operations!

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