Solve the inequality.
5+7x≥11x+3−4x
(1 point)
Responses
No Solution
No Solution
x≤2
x is less than or equal to 2
All real numbers
All real numbers
x≤−2
x≤2
To solve the inequality, we need to simplify and combine like terms on both sides of the inequality.
Starting with the left side, we have:
5 + 7x
And on the right side, we have:
11x + 3 - 4x
Combining like terms, we get:
5 + 3 - 7x + 11x - 4x
Simplifying further, we have:
8 - 7x + 11x - 4x
Simplifying again, we get:
8 - 7x + 11x - 4x = 8
Now we have the simplified inequality:
8 = 8
Since 8 is always equal to itself, the inequality is true for all values of x. Therefore, the solution is:
x ≤ -2
To solve the inequality, we need to isolate the variable x on one side of the inequality symbol. Let's simplify the equation step by step:
5 + 7x ≥ 11x + 3 - 4x
First, let's combine like terms on both sides of the inequality:
5 + 7x ≥ 7x + 3
Next, let's subtract 7x from both sides to get rid of the term with x on the right side:
5 ≥ 3
Since 5 is greater than or equal to 3, this inequality holds true.
Now, let's look at the answer choices provided:
- "No Solution" means that there is no value of x that satisfies the given inequality. However, in our case, we found a valid solution, so this choice is incorrect.
- "x ≤ 2" means that any value of x less than or equal to 2 would satisfy the inequality. This is valid since the inequality holds true for any value of x, including x = 2. Therefore, this is a valid solution.
- "All real numbers" means that any value of x, regardless of its magnitude, would satisfy the inequality. In our case, since the inequality holds true for any value of x, this is also a valid solution.
- "x ≤ -2" means that any value of x less than or equal to -2 would satisfy the inequality. However, we did not find this as a solution during our simplification steps. Therefore, this choice is incorrect.
In conclusion, the correct solution to the inequality is:
x ≤ 2