9c + 1 > 10 . i don’t get this
The Correct Answer and Explanation is:
To solve the inequality:
9c + 1 > 10
Start by isolating the variable term:
Step 1: Subtract 1 from both sides
9c + 1 − 1 > 10 − 1
9c > 9
Step 2: Divide both sides by 9
9c ÷ 9 > 9 ÷ 9
c > 1
Final Answer:
c > 1
Explanation (300 words):
This inequality represents a mathematical statement where a linear expression is greater than a constant. To find the solution, apply operations that simplify the expression while maintaining the truth of the inequality.
Begin by addressing the constant on the left-hand side. The goal is to isolate the variable term. The original inequality has a constant value of +1 added to the term 9c. To eliminate this +1, subtract 1 from both sides of the inequality. This creates a new expression: 9c > 9. This step simplifies the inequality and moves closer to solving for the variable.
Next, examine the coefficient attached to the variable. The coefficient of c is 9, which means the variable is being multiplied by 9. To isolate the variable completely, divide both sides of the inequality by 9. Division is the inverse of multiplication and is used to cancel out the coefficient. Dividing both sides results in the simplified expression: c > 1.
This expression means that the variable c must be greater than 1 for the original inequality to be true. Any number greater than 1—such as 1.5, 2, or 10—will satisfy the inequality. If c equals 1, the left-hand side would evaluate to 9(1) + 1 = 10, which is not greater than 10, so c = 1 does not satisfy the inequality. Only values strictly greater than 1 make the statement true.
The solution set includes all real numbers greater than 1. This type of inequality describes an open interval on a number line starting just above 1 and extending infinitely to the right.
