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

Step 1: Understanding the Concept:
This is a simple linear inequality in one variable. Solving it involves applying arithmetic operations to both sides of the inequality to isolate the variable $x$, similar to solving a linear equation.

Step 2: Key Formula or Approach:
Use the properties of inequalities. You can add or subtract the same value from both sides without changing the inequality sign. Group the terms containing $x$ on one side and the constant terms on the other side.

Step 3: Detailed Explanation:
The given linear inequality is: \[ 3x - 5<2x - 4 \] To collect all the $x$ terms on the left side, subtract $2x$ from both sides: \[ 3x - 2x - 5<2x - 2x - 4 \] \[ x - 5<-4 \] Now, to isolate $x$, add $5$ to both sides of the inequality: \[ x - 5 + 5<-4 + 5 \] \[ x<1 \] This means any real number less than $1$ is a valid solution for the given inequality.

Step 4: Final Answer:
The solution is $x<1$.