The linear equation px−5=−x+15/3
 , where x
 is a variable and p
 is a constant, is true for all values of x
. Which of the following is the value of 3p+1
 ?

Given the linear equation \( px - 5 = -x + \frac{15}{3} \), where \(x\) is a variable and \(p\) is a constant, we want to find the value of \(3p + 1\).

### Step 1: Simplify the equation
First, simplify the right side of the equation:
\[
\frac{15}{3} = 5
\]
So, the equation becomes:
\[
px - 5 = -x + 5
\]

### Step 2: Rearrange the equation
Next, let's bring all terms involving \(x\) to one side of the equation and constant terms to the other side:
\[
px + x = 5 + 5
\]
Combine like terms:
\[
(p + 1)x = 10
\]

### Step 3: Analyze the equation
Since the equation is true for all values of \(x\), the coefficient of \(x\) on both sides must be equal, and the constant terms on both sides must also be equal.

1. **Coefficient of \(x\)**:
   \[
   p + 1 = 0
   \]
   Solving for \(p\):
   \[
   p = -1
   \]

### Step 4: Calculate \(3p + 1\)
Now, substitute \(p = -1\) into \(3p + 1\):
\[
3p + 1 = 3(-1) + 1 = -3 + 1 = -2
\]

So, the value of \(3p + 1\) is \(-2\).

Would you like further details or have any other questions?

Here are 5 related questions:
1. How would the solution change if the equation had a different constant term on the right side?
2. What is the significance of an equation being true for all values of \(x\)?
3. Can you explain the steps to solve linear equations with variables on both sides in more detail?
4. What happens to the equation if we substitute different values for \(p\)?
5. How would you solve the equation if it included fractions on both sides?

**Tip:** When a linear equation is true for all values of a variable, focus on equating the coefficients of the variable and the constant terms separately. This approach will help you solve for any unknown constants.

Learn how to solve the linear equation px - 5 = -x + 5 to find the value of 3p + 1. This problem explores concepts in linear equations, variables, and constants. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation