Solve the Linear Equation: Finding X in -8x+3=-29

Q: Why do I subtract 3 from both sides first?

You want to isolate the x term by getting rid of the constant +3 on the left side. Subtracting 3 from both sides keeps the equation balanced and gives you $ -8x = -32 $.

Q: What happens when I divide two negative numbers?

When you divide negative by negative, you get positive! So $ \frac{-32}{-8} = +4 $. Remember: negative ÷ negative = positive.

Q: How do I know which operations to do first?

Follow the reverse order of operations! Since addition/subtraction come after multiplication/division in PEMDAS, you undo addition first, then division.

Q: What if I get a different answer when I check?

If substituting doesn't work, you made an error somewhere. Go back step by step and check your arithmetic, especially with negative signs!

Q: Can I add 29 to both sides instead of subtracting 3?

You could, but it's less efficient! You'd get $ -8x + 32 = 0 $, then subtract 32. It's easier to eliminate the smaller constant first.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown X

00:07 Let's arrange the equation so that one side has only the unknown X

00:15 Let's simplify what we can

00:24 Let's isolate the unknown X and calculate

00:42 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

Solve for X:

$-8x+3=-29$

2

Step-by-step solution

To solve the equation $-8x + 3 = -29$ , we'll follow these steps:

Step 1: Subtract 3 from both sides of the equation to eliminate the constant on the left side.
Step 2: Divide both sides by $-8$ , the coefficient of $x$ , to solve for $x$ .

Let's apply these steps:
Step 1: Subtract 3 from both sides:
$-8x + 3 - 3 = -29 - 3$
This simplifies to:
$-8x = -32$

Step 2: Divide both sides by $-8$ to isolate $x$ :
$\frac{-8x}{-8} = \frac{-32}{-8}$
This results in:
$x = 4$

Therefore, the solution to the equation is $x = 4$ , which corresponds to choice 4.

3

Final Answer

4

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Move constants first, then divide by coefficient
Technique: Subtract 3: $-8x + 3 - 3 = -29 - 3$
Check: Substitute x = 4: $-8(4) + 3 = -32 + 3 = -29$ ✓

Common Mistakes

Avoid these frequent errors

Dividing by the wrong sign
Don't divide -32 by 8 instead of -8 = wrong answer of -4! When the coefficient is negative like -8x, you must divide by the full coefficient including the negative sign. Always divide both sides by exactly what multiplies x.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do I subtract 3 from both sides first?

+

You want to isolate the x term by getting rid of the constant +3 on the left side. Subtracting 3 from both sides keeps the equation balanced and gives you $-8x = -32$ .

What happens when I divide two negative numbers?

+

When you divide negative by negative, you get positive! So $\frac{-32}{-8} = +4$ . Remember: negative ÷ negative = positive.

How do I know which operations to do first?

+

Follow the reverse order of operations! Since addition/subtraction come after multiplication/division in PEMDAS, you undo addition first, then division.

What if I get a different answer when I check?

+

If substituting doesn't work, you made an error somewhere. Go back step by step and check your arithmetic, especially with negative signs!

Can I add 29 to both sides instead of subtracting 3?

+

You could, but it's less efficient! You'd get $-8x + 32 = 0$ , then subtract 32. It's easier to eliminate the smaller constant first.

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Solve the Linear Equation: Finding X in -8x+3=-29

Linear Equations with Negative Coefficients

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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 subtract 3 from both sides first?

What happens when I divide two negative numbers?

How do I know which operations to do first?

What if I get a different answer when I check?

Can I add 29 to both sides instead of subtracting 3?

🌟 Unlock Your Math Potential

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