9c + 1 = 10 solve the equations
The Correct Answer and Explanation is:
To solve the equation:
9c + 1 = 10
Follow these algebraic steps:
Step 1: Eliminate the constant on the left side
Subtract 1 from both sides of the equation:9c+1−1=10−19c + 1 – 1 = 10 – 19c+1−1=10−19c=99c = 99c=9
Step 2: Isolate the variable
Divide both sides of the equation by 9:9c9=99\frac{9c}{9} = \frac{9}{9}99c=99c=1c = 1c=1
Final Answer:
c = 1
Explanation (300 words):
Solving linear equations involves isolating the unknown variable using inverse operations. The equation provided is in the form of a one-step linear equation with an added constant term. The goal is to determine the value of c that makes the equation true.
Starting with 9c + 1 = 10, the constant +1 is located on the same side as the variable term 9c. To simplify, the first step is to remove this constant by performing the opposite operation—in this case, subtraction. Subtracting 1 from both sides eliminates the +1 and balances the equation. This operation yields 9c = 9.
At this stage, the equation has been reduced to a simpler form where the coefficient 9 multiplies the variable c. To solve for c, the coefficient must be removed by applying the inverse operation of multiplication, which is division. Dividing both sides of the equation by 9 eliminates the coefficient and isolates the variable.
This final step results in c = 1. Substituting 1 back into the original equation verifies the correctness:
9(1) + 1 = 9 + 1 = 10, which confirms that the solution satisfies the original expression.
The method used here applies to any similar linear equation: isolate the variable by removing constants and coefficients through appropriate inverse operations, ensuring each step maintains equality across both sides.
