Solve the inequality, and graph the solution on a number line. 5x - 5 <= 5(x - 1)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution is _.
(Type an inequality. Simplify your answer.)
O B. The solution is all real numbers.
O C. There is no solution.
To solve the inequality, we can start by simplifying both sides:
5x - 5 <= 5(x - 1)
5x - 5 <= 5x - 5
Next, we can subtract 5x from both sides:
-5 <= -5
Since -5 is less than or equal to -5, the inequality holds true for all values of x. Therefore, the solution is:
O B. The solution is all real numbers.
To solve the inequality 5x - 5 <= 5(x - 1), we will first simplify the equation:
5x - 5 <= 5x - 5
Notice that the terms on both sides are identical. This means that the inequality is true for all values of x. Therefore, the solution is all real numbers.
So, the correct choice is:
O B. The solution is all real numbers.
To solve the inequality 5x - 5 <= 5(x - 1), we need to simplify the expression on both sides of the inequality sign and solve for x.
Let's start by simplifying both sides of the inequality:
5x - 5 <= 5x - 5
On the left side, there are no changes because the expression is already simplified.
On the right side, we can distribute the 5 into the parentheses:
5x - 5 <= 5x - 5
Now, let's simplify further:
5x - 5 <= 5x - 5
The equation becomes:
5x - 5 <= 5x - 5
Next, we can isolate the variable x:
Subtracting 5x from both sides:
-5 <= -5
Since -5 is always less than or equal to -5, the inequality is satisfied for all real numbers. Therefore, the solution to the inequality 5x - 5 <= 5(x - 1) is all real numbers.
Therefore, the correct choice is:
B. The solution is all real numbers.