Question
Write an algebraic equation and use it to solve the problem Three-fourths of a number is -21 . What is the numbe
Ask by Hall Williams. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The number is -28.
Solution
Sure! Let's solve the problem step by step by setting up an algebraic equation.
**Problem Statement:**
Three-fourths of a number is -21. What is the number?
**Step 1: Define the Variable**
Let’s denote the unknown number as \( x \).
**Step 2: Translate the Problem into an Equation**
The phrase "three-fourths of a number is -21" can be written algebraically as:
\[
\frac{3}{4}x = -21
\]
**Step 3: Solve for \( x \)**
To find the value of \( x \), follow these steps:
1. **Isolate \( x \):**
\[
\frac{3}{4}x = -21
\]
2. **Multiply both sides by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\):**
\[
x = -21 \times \frac{4}{3}
\]
3. **Calculate the right-hand side:**
\[
x = -21 \times \frac{4}{3} = -28
\]
**Conclusion:**
The number is **-28**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Let the unknown number be represented by the variable \( x \). We can set up the equation as follows: \[ \frac{3}{4}x = -21 \] To solve for \( x \), we need to isolate it. We can do this by multiplying both sides of the equation by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\): \[ x = -21 \times \frac{4}{3} = -28 \] So the number is \(-28\). Now, let's check the result by substituting \(-28\) back into the equation: \[ \frac{3}{4} \times -28 = -21 \] This holds true, confirming that \(-28\) is indeed the solution!
