Solve Linear Equation: 5(8+a)-(2a+14)=56 Using Distribution

Q: Why do I need to distribute the negative sign to both terms?

The negative sign in front of parentheses acts like multiplying by -1. Just like 3(x+2) = 3x+6, we have -(x+2) = -x-2. Every term inside gets the opposite sign!

Q: What if I mess up the distributive property?

Take it step by step! Write out each multiplication separately: 5×8, 5×a, then (-1)×2a, (-1)×14. This prevents sign errors and keeps your work organized.

Q: How do I combine like terms after distributing?

Look for terms with the same variable. In this problem, 5a and -2a are like terms, so 5a-2a = 3a. Constants 40 and -14 combine to give 26.

Q: What if my final answer doesn't match any of the multiple choice options?

Double-check your distributive property and sign work first! Most errors happen there. Then verify by substituting your answer back into the original equation.

Q: Is there a faster way to solve this without distributing?

Distributing is actually the most reliable method here! Other shortcuts might work sometimes, but the distributive property ensures you handle all terms correctly every time.

Linear Equations with Distributive Property

Solve the following equation:

$5(8+a)-(2a+14)=56$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Open brackets properly, multiply by each term

00:15 Collect like terms

00:25 Arrange the equation so that only the unknown A is on one side

00:35 Isolate A

00:39 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$5(8+a)-(2a+14)=56$

Step-by-step solution

Let's open the parentheses using the distributive property and use the formula:

$a(x+b)=ax+ab$

$40+5a-2a-14=56$

We'll substitute the terms accordingly:

$26+3a=56$

We'll move 26 to the right side and keep the appropriate sign:

$3a=56-26$

$3a=30$

We'll divide both sides by 3:

$\frac{3a}{3}=\frac{30}{3}$

$a=10$

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Distributive Rule: Apply a(x+b) = ax + ab to both positive and negative terms
Technique: 5(8+a) becomes 40+5a and -(2a+14) becomes -2a-14
Check: Substitute a=10: 5(8+10)-(2×10+14) = 90-34 = 56 ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign when distributing
Don't distribute -(2a+14) as -2a+14 = wrong signs! The negative affects BOTH terms inside parentheses. Always distribute the negative to get -2a-14.

Practice Quiz

Test your knowledge with interactive questions

Solve for x:

$$ 2(4-x)=8 $$

FAQ

Everything you need to know about this question

Why do I need to distribute the negative sign to both terms?

The negative sign in front of parentheses acts like multiplying by -1. Just like 3(x+2) = 3x+6, we have -(x+2) = -x-2. Every term inside gets the opposite sign!

What if I mess up the distributive property?

Take it step by step! Write out each multiplication separately: 5×8, 5×a, then (-1)×2a, (-1)×14. This prevents sign errors and keeps your work organized.

How do I combine like terms after distributing?

Look for terms with the same variable. In this problem, 5a and -2a are like terms, so 5a-2a = 3a. Constants 40 and -14 combine to give 26.

Why do we move 26 to the right side instead of moving 56 left?

Both work! Moving the constant to the right side (3a = 56-26) is often easier because we end up with positive numbers, making the arithmetic simpler.

What if my final answer doesn't match any of the multiple choice options?

Double-check your distributive property and sign work first! Most errors happen there. Then verify by substituting your answer back into the original equation.

Is there a faster way to solve this without distributing?

Distributing is actually the most reliable method here! Other shortcuts might work sometimes, but the distributive property ensures you handle all terms correctly every time.

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