When 3x is multiplied by 5 and then increased by 3, the result is less than 48. What is the largest possible integer value for x?

We are given the inequality:

\[
5 \times 3x + 3 < 48
\]

Let's solve this step by step.

### Step 1: Distribute and simplify the expression
First, multiply \( 3x \) by 5:

\[
15x + 3 < 48
\]

### Step 2: Isolate the term with \( x \)
Subtract 3 from both sides to get:

\[
15x < 45
\]

### Step 3: Solve for \( x \)
Now, divide both sides by 15:

\[
x < 3
\]

### Step 4: Determine the largest possible integer value for \( x \)
The largest integer that satisfies this inequality is \( x = 2 \).

Thus, the largest possible integer value for \( x \) is **2**.

Would you like any more details or have any questions?

Here are five related questions for further practice:

1. What if the expression was \( 5 \times 3x + 6 \) instead of \( 5 \times 3x + 3 \)? What would be the largest integer value for \( x \)?
2. If the result had to be less than or equal to 48, what would the largest integer value for \( x \) be?
3. What if the inequality was \( 5 \times 3x + 3 \leq 50 \)? What would \( x \) be?
4. If the inequality was changed to \( 4 \times 3x + 3 < 48 \), how would the solution change?
5. How would the solution change if the inequality was \( 10 \times 3x + 3 < 48 \)?

**Tip:** When solving inequalities, carefully isolate the variable step by step, just as you would in solving equations, and then consider the direction of the inequality when determining the final answer.

Learn how to solve inequalities involving multiplication and addition step-by-step. Given the inequality 5 times 3x plus 3 is less than 48, find the largest possible integer value for x. Explore related questions for further practice.

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