Solve c-5.3=-6.4 . Write your answer as a decimal to the nearest tenth
The Correct Answer and Explanation is:
To solve the equation c−5.3=−6.4c – 5.3 = -6.4c−5.3=−6.4, we aim to isolate ccc on one side of the equation. Here’s the step-by-step solution:
Step 1: Isolate ccc
Add 5.3 to both sides of the equation to eliminate the subtraction of 5.3:c−5.3+5.3=−6.4+5.3c – 5.3 + 5.3 = -6.4 + 5.3c−5.3+5.3=−6.4+5.3
This simplifies to:c=−1.1c = -1.1c=−1.1
Final Answer:
c=−1.1c = -1.1c=−1.1
Explanation:
This equation involves a basic operation where a number is subtracted from the variable ccc. The goal is to determine the value of ccc that makes the equation true.
- Understanding the Equation:
The equation c−5.3=−6.4c – 5.3 = -6.4c−5.3=−6.4 means that when 5.3 is subtracted from some number ccc, the result is -6.4. To “undo” the subtraction and find ccc, we must perform the opposite operation, which is addition. - Adding 5.3 to Both Sides:
By adding 5.3 to both sides, we maintain the balance of the equation (a fundamental principle in algebra). This step eliminates the -5.3 on the left-hand side, leaving ccc alone. - Performing the Arithmetic:
Adding the numbers −6.4+5.3-6.4 + 5.3−6.4+5.3:- When working with decimals, align them and subtract since the numbers have opposite signs.
- The absolute value of -6.4 is 6.4, and that of 5.3 is 5.3. Subtracting 5.3 from 6.4 gives 1.1.
- The larger absolute value is from -6.4, so the result is negative: −1.1-1.1−1.1.
- Result Verification:
Substitute c=−1.1c = -1.1c=−1.1 back into the original equation to check:−1.1−5.3=−6.4-1.1 – 5.3 = -6.4−1.1−5.3=−6.4The equation holds true, confirming the solution.
By isolating ccc and carefully performing decimal arithmetic, we find that c=−1.1c = -1.1c=−1.1.