Solve the inequality, and graph the solution on a number line.
2x−2≤2(x−1)
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Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The solution is enter your response here.
(Type an inequality. Simplify your answer.)
B.The solution is all real numbers.
The solution is all real numbers.
C.There is no solution.
There is no solution.
To solve the inequality 2x - 2 ≤ 2(x - 1), we need to simplify and find the range of x that satisfies the inequality.
2x - 2 ≤ 2(x - 1)
2x - 2 ≤ 2x - 2
Now, we can see that the inequality 2x - 2 ≤ 2x - 2 is always true, regardless of the value of x. This means that the solution to the inequality is all real numbers.
The solution is: B. The solution is all real numbers.
To solve the inequality 2x - 2 ≤ 2(x - 1), we will simplify the expression and determine the solution.
Step 1: Distribute 2 to (x - 1) inside the parentheses.
2x - 2 ≤ 2x - 2
Step 2: Subtract 2x from both sides to isolate the variable.
-2 ≤ -2
Step 3: The inequality -2 ≤ -2 is true for all values of x. Therefore, the solution is all real numbers.
Answer: B. The solution is all real numbers.
To solve the inequality 2x-2 ≤ 2(x-1), we can follow these steps:
Step 1: Distribute the 2 on the right side of the inequality:
2x-2 ≤ 2x-2
Step 2: Combine like terms:
2x-2 ≤ 2x-2
Step 3: Subtract 2x from both sides:
-2 ≤ -2
Step 4: Simplify:
-2 ≤ -2
The inequality -2 ≤ -2 is always true, no matter the value of x. This means that any value of x will satisfy the inequality.
Therefore, the solution to the inequality is B. The solution is all real numbers.