Solve the Algebraic Equation: 5 - (3b - 1) = 0

Q: Why does the -1 become +1 when I distribute?

When you distribute a negative sign through parentheses, you multiply each term by -1. So -(-1) = +1. Think of it as: $ -(3b - 1) = -3b + 1 $.

Q: What if I forget to combine like terms first?

You'll make the problem harder! Always simplify first by combining constants (5 + 1 = 6) before trying to isolate the variable. This reduces mistakes.

Q: Can I add 3b to both sides instead of subtracting 6?

Yes! From $ 6 - 3b = 0 $, you can add 3b to get $ 6 = 3b $, then divide by 3. Both methods give b = 2.

Q: What does it mean when the equation equals zero?

Setting an equation equal to zero means you're finding the root or solution where the expression has no value. This is very common in algebra!

Linear Equations with Distribution and Simplification

$5-(3b-1)=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solution

00:03 Open parentheses properly, multiply by each factor

00:17 Collect terms

00:24 Arrange the equation so that only the unknown B is on one side

00:34 Isolate B

00:40 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

$5-(3b-1)=0$

Step-by-step solution

To solve the given linear equation $5 - (3b - 1) = 0$ , follow these steps:

Step 1: Simplify the equation.
Start by distributing the negative sign through the parentheses:
$5 - 3b + 1 = 0$
Step 2: Combine like terms.
Combine the constant terms on the left side:
$6 - 3b = 0$
Step 3: Isolate the variable $b$ .
Subtract 6 from both sides of the equation to isolate the term with $b$ :
$-3b = -6$
Step 4: Solve for $b$ .
Divide both sides by -3 to solve for $b$ :
$b = \frac{-6}{-3} = 2$

Therefore, the solution to the equation is $b = 2$ .

Final Answer

$b=2$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Apply negative sign to all terms inside parentheses
Technique: Combine like terms: 5 + 1 = 6 before isolating variable
Check: Substitute b = 2: 5 - (3(2) - 1) = 5 - 5 = 0 ✓

Common Mistakes

Avoid these frequent errors

Incorrectly distributing the negative sign
Don't change 5 - (3b - 1) to 5 - 3b - 1 = wrong answer! This gives 4 - 3b = 0, so b = 4/3 instead of b = 2. Always distribute the negative to ALL terms: 5 - 3b + 1.

Practice Quiz

Test your knowledge with interactive questions

$$ 5x=1 $$

What is the value of x?

FAQ

Everything you need to know about this question

Why does the -1 become +1 when I distribute?

When you distribute a negative sign through parentheses, you multiply each term by -1. So -(-1) = +1. Think of it as: $-(3b - 1) = -3b + 1$ .

What if I forget to combine like terms first?

You'll make the problem harder! Always simplify first by combining constants (5 + 1 = 6) before trying to isolate the variable. This reduces mistakes.

Can I add 3b to both sides instead of subtracting 6?

Yes! From $6 - 3b = 0$ , you can add 3b to get $6 = 3b$ , then divide by 3. Both methods give b = 2.

How do I know when to distribute vs. when to divide?

Look at the equation structure! When you see parentheses with a number or sign in front, distribute first. Only divide when you have a coefficient directly attached to your variable.

What does it mean when the equation equals zero?

Setting an equation equal to zero means you're finding the root or solution where the expression has no value. This is very common in algebra!

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