Solve (a+3a)(5+2)=112: Find the Value of Variable a

Linear Equations with Parenthetical Expressions

(a+3a)×(5+2)=112 (a+3a)\times(5+2)=112

Calculate a a

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find A
00:03 Make sure to open parentheses properly
00:07 Each term in parentheses multiplies each term in the second parentheses
00:27 Solve each multiplication and then add
00:43 Solve one addition operation at a time
01:02 Isolate A
01:12 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

(a+3a)×(5+2)=112 (a+3a)\times(5+2)=112

Calculate a a

2

Step-by-step solution

We begin by solving the two exercises inside of the parentheses:

4a×7=112 4a\times7=112

We then divide each of the sections by 4:

4a×74=1124 \frac{4a\times7}{4}=\frac{112}{4}

In the fraction on the left side we simplify by 4 and in the fraction on the right side we divide by 4:

a×7=28 a\times7=28

Remember that:

a×7=a7 a\times7=a7

Lastly we divide both sections by 7:

a77=287 \frac{a7}{7}=\frac{28}{7}

a=4 a=4

3

Final Answer

4

Key Points to Remember

Essential concepts to master this topic
  • Simplify First: Always solve expressions inside parentheses before proceeding
  • Technique: Combine like terms: a + 3a = 4a, then 4a × 7 = 28a
  • Check: Substitute a = 4: (4 + 12) × 7 = 16 × 7 = 112 ✓

Common Mistakes

Avoid these frequent errors
  • Solving without simplifying parentheses first
    Don't try to distribute or solve before simplifying (a + 3a) and (5 + 2) = wrong approach! This creates unnecessary complexity and leads to errors. Always simplify expressions inside parentheses first: (a + 3a) = 4a and (5 + 2) = 7.

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 simplify the parentheses first instead of distributing?

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Simplifying first makes the problem much easier! (a + 3a) = 4a and (5 + 2) = 7, so you get the clean equation 4a×7=112 4a \times 7 = 112 instead of a messy distribution.

How do I combine like terms like a + 3a?

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Think of it like counting: a + 3a = 1a + 3a = 4a. Just add the coefficients (numbers in front) together. It's like saying 1 apple + 3 apples = 4 apples!

What if I get a different answer when I check?

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If substituting your answer doesn't work, go back and check your arithmetic. Make sure you simplified the parentheses correctly and divided both sides by the same number.

Can I solve this equation in a different order?

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While you could distribute first, it's much more efficient to simplify parentheses first. This keeps the numbers smaller and reduces chances for calculation errors.

What does 'combine like terms' actually mean?

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  • Like terms have the same variable part
  • In (a + 3a), both terms have 'a'
  • Add their coefficients: 1 + 3 = 4
  • Result: 4a 4a

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