Decreasing half of a number by 19.7 results in –4.1. What is the number?

Use the given equation to find the number.

One-halfx – 19.7 = –4.1

What is the number?

Let's solve the equation step by step.

Given equation:
\[
\frac{1}{2}x - 19.7 = -4.1
\]

### Step 1: Add 19.7 to both sides of the equation to isolate the term with \( x \).
\[
\frac{1}{2}x - 19.7 + 19.7 = -4.1 + 19.7
\]
\[
\frac{1}{2}x = 15.6
\]

### Step 2: Multiply both sides by 2 to solve for \( x \).
\[
x = 15.6 \times 2
\]
\[
x = 31.2
\]

So, the number is \( \boxed{31.2} \).

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How would you solve a similar equation if the subtraction were addition?
2. What is the result if you multiply half of 31.2 by 19.7?
3. How do you check if the calculated number satisfies the original equation?
4. How do linear equations like this one apply in real-world situations?
5. What happens if the original number were negative?
6. How would the solution change if instead of subtracting 19.7, you add it?
7. Can you generalize the solution for any number \( y \) instead of 19.7?
8. How would the steps differ if you had \( \frac{2}{3}x \) instead of \( \frac{1}{2}x \)?

**Tip:** Always verify your solution by substituting it back into the original equation.

Learn how to solve a linear equation involving fractions and decimals step-by-step. This problem includes concepts such as isolating variables and basic arithmetic operations. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation