Question

The solution of $3x - 5<2x - 4$ is

• A. $x<1$
• B. $x>-1$
• C. $x<9$
• D. $x>9$

Hint:

Treat linear inequalities just like linear equations when adding or subtracting terms across the inequality symbol. Remember that the inequality symbol only flips direction if you multiply or divide both sides by a negative number.

Answer 1

The Correct Option is A

To solve the inequality \(3x - 5 < 2x - 4\), we need to isolate \(x\). We'll do this step by step:

1. First, subtract \(2x\) from both sides of the inequality to get:

\(3x - 5 - 2x < 2x - 4 - 2x\)

1. This simplifies to:

\(x - 5 < -4\)

1. Next, add 5 to both sides to isolate \(x\):

\(x - 5 + 5 < -4 + 5\)

1. Which gives us:

\(x < 1\)

Thus, the solution to the inequality is \(x < 1\).

To verify, we can substitute a number less than 1 into the original inequality:

• If \(x = 0\), then:

\(3(0) - 5 < 2(0) - 4\)

• Evaluates to:

\(-5 < -4\)

This is true. Therefore, the solution \(x < 1\) is correct.

We have successfully solved the given inequality, and the correct answer is \(x < 1\).