Solve the Linear Equation: 3-(x-4)+8x=14 Step by Step

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

The negative sign acts like multiplying by -1. Just like $ -1(x-4) = -1x + (-1)(-4) = -x + 4 $. If you forget to distribute to both terms, you'll get the wrong equation!

Q: What if I get confused with all the signs?

Take it step by step! First distribute completely, then rewrite the equation clearly with all terms. Use parentheses around negative terms if it helps: 3 + (-x) + 4 + 8x = 14.

Q: How can I check my work without substituting back?

You can work backwards! Start with $ 7x = 7 $ and add 7 to both sides: $ 7 + 7x = 14 $. Then expand back to the original form to verify your algebra.

Q: Is there a faster way to solve this type of equation?

With practice, you can combine steps! But when learning, always show each step clearly. Distribution errors are very common, so being careful is more important than being fast.

Linear Equations with Distribution and Combining

Solve for X:

$3-(x-4)+8x=14$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 We want to isolate the unknown X

00:07 Open brackets properly, multiply by each factor

00:10 Negative times positive is always negative

00:19 Negative times negative is always positive

00:28 Collect like terms

00:43 Isolate the unknown X

00:54 Simplify what we can

00:59 Isolate the unknown X

01:13 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

Solve for X:

$3-(x-4)+8x=14$

Step-by-step solution

To solve the equation $3 - (x - 4) + 8x = 14$ , we will simplify and solve for $x$ step-by-step:

Step 1: Distribute the negative sign inside the parentheses:
$- (x - 4) = -x + 4$ .
Step 2: Rewrite the equation with the distributed terms:
$3 + (-x + 4) + 8x = 14$ .
Step 3: Simplify by combining like terms:
Combine the constants: $3 + 4 = 7$
Combine the $x$ terms: $-x + 8x = 7x$ .
This gives us $7 + 7x = 14$ .
Step 4: Isolate the $x$ term:
Subtract 7 from both sides: $7x = 14 - 7$ .
This simplifies to $7x = 7$ .
Step 5: Solve for $x$ by dividing both sides by 7:
$x = \frac{7}{7}$ .
Simplifying gives $x = 1$ .

Therefore, the solution to the equation is $x = 1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Apply negative sign to every term inside parentheses
Technique: Combine like terms: constants (3+4=7) and variables (-x+8x=7x)
Check: Substitute x=1: 3-(1-4)+8(1) = 3+3+8 = 14 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute the negative sign
Don't write -(x-4) as -x-4 = wrong distribution! This gives you 3-x-4+8x=2+7x=14, leading to x=12/7. Always distribute the negative to get -x+4, making the equation 3-x+4+8x=14.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

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

The negative sign acts like multiplying by -1. Just like $-1(x-4) = -1x + (-1)(-4) = -x + 4$ . If you forget to distribute to both terms, you'll get the wrong equation!

How do I combine like terms correctly?

Group constants together and variables together. In this problem: constants are 3 and +4 (from distribution), giving 7. Variables are -x and +8x, giving 7x.

What if I get confused with all the signs?

Take it step by step! First distribute completely, then rewrite the equation clearly with all terms. Use parentheses around negative terms if it helps: 3 + (-x) + 4 + 8x = 14.

How can I check my work without substituting back?

You can work backwards! Start with $7x = 7$ and add 7 to both sides: $7 + 7x = 14$ . Then expand back to the original form to verify your algebra.

Is there a faster way to solve this type of equation?

With practice, you can combine steps! But when learning, always show each step clearly. Distribution errors are very common, so being careful is more important than being fast.

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