Solve.
5 left parenthesis x minus 4 right parenthesis less than 2 left parenthesis 3 x minus 1 right parenthesis

Let's solve the inequality:

\[ 5(x - 4) < 2(3x - 1) \]

### Step 1: Distribute the constants on both sides
Expand both sides of the inequality:

\[
5(x - 4) = 5x - 20
\]
\[
2(3x - 1) = 6x - 2
\]

Now the inequality becomes:

\[
5x - 20 < 6x - 2
\]

### Step 2: Move all \(x\)-terms to one side
Subtract \(5x\) from both sides:

\[
-20 < x - 2
\]

### Step 3: Isolate \(x\)
Add 2 to both sides to isolate \(x\):

\[
-20 + 2 < x
\]
\[
-18 < x
\]

### Final answer:
\[
x > -18
\]

This is the solution to the inequality.

Would you like more details or have any questions?

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Here are 5 related questions to expand on this topic:

1. How do you solve inequalities with variables on both sides?
2. What happens if you multiply or divide an inequality by a negative number?
3. How can you graph the solution \(x > -18\) on a number line?
4. What are the key differences between solving equations and solving inequalities?
5. Can inequalities have more than one solution?

**Tip:** When solving inequalities, remember that multiplying or dividing by a negative number reverses the inequality sign.

Learn how to solve the linear inequality 5(x - 4) < 2(3x - 1) with step-by-step instructions. This problem covers key algebraic concepts, including inequalities, the distributive property, and the transposition rule. Ideal for students in Grades 8-10.

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