Solve Linear Inequality: 6x - 4 < 14 Step-by-Step

Q: When do I flip the inequality sign?

You only flip the inequality sign when multiplying or dividing by a negative number. Since we divided by positive 6, the sign stays the same!

Q: Why isn't the answer exactly x = 3?

Because we have an inequality (less than 3, like 2.5, 1, or even -10!

Q: How do I check if x = 2.5 works?

Substitute: $ 6(2.5) - 4 = 15 - 4 = 11 $. Since 11

Q: What does the fraction 9/3 in the answer choice mean?

The fraction $ \frac{9}{3} $ simplifies to 3, so \( x is the same as \( x . Both are correct ways to write the answer!

Q: Can x equal exactly 3?

No! The inequality uses strictly less than 3, meaning 3 itself is not included.

Linear Inequalities with One-Step Operations

Solve the inequality:

$6x - 4 < 14$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the inequality:

$6x - 4 < 14$

Step-by-step solution

To solve the inequality $6x - 4 < 14$ , follow these steps:

1. Add 4 to both sides:

$6x - 4 + 4 < 14 + 4$

2. Simplify:

$6x < 18$

3. Divide both sides by 6 to solve for $x$ :

$x < \frac{18}{6}$

4. This simplifies to:

$x < 3$

Thus, the solution is $x < 3$ .

Final Answer

$x < \frac{9}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Apply same operation to both sides to maintain inequality
Technique: Add 4 first: 6x - 4 + 4 < 14 + 4
Check: Test x = 2: 6(2) - 4 = 8 < 14 ✓

Common Mistakes

Avoid these frequent errors

Flipping inequality sign when dividing by positive numbers
Don't flip < to > when dividing by positive 6 = wrong direction! The inequality sign only flips when multiplying or dividing by negative numbers. Always keep the same direction when dividing by positive numbers.

Practice Quiz

Test your knowledge with interactive questions

Solve the following inequality:

$3x+4 \leq 10$

FAQ

Everything you need to know about this question

When do I flip the inequality sign?

You only flip the inequality sign when multiplying or dividing by a negative number. Since we divided by positive 6, the sign stays the same!

Why isn't the answer exactly x = 3?

Because we have an inequality (< symbol), not an equation (= symbol). This means x can be any number less than 3, like 2.5, 1, or even -10!

How do I check if x = 2.5 works?

Substitute: $6(2.5) - 4 = 15 - 4 = 11$ . Since 11 < 14 is true, x = 2.5 is part of the solution!

What does the fraction 9/3 in the answer choice mean?

The fraction $\frac{9}{3}$ simplifies to 3, so $x < \frac{9}{3}$ is the same as $x < 3$ . Both are correct ways to write the answer!

Can x equal exactly 3?

No! The inequality uses < (less than), not ≤ (less than or equal to). So x must be strictly less than 3, meaning 3 itself is not included.

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