Write and solve an inequality that represents the numbers that are not solutions of each inequality.
a. x-7 less than or equal to -10
Sure! Let's solve for the numbers that are not solutions of the inequality x - 7 ≤ -10.
First, we add 7 to both sides of the inequality to isolate the variable:
x ≤ -10 + 7
x ≤ -3
Now, let's find the numbers that are not solutions of this inequality. Since x has to be less than or equal to -3, any number greater than -3 will not be a solution.
So, the inequality that represents the numbers that are not solutions is:
x > -3
To represent the numbers that are not solutions of the inequality x - 7 ≤ -10, we first need to find the solutions.
Step 1: Solve the inequality:
x - 7 ≤ -10
Adding 7 to both sides:
x - 7 + 7 ≤ -10 + 7
x ≤ -3
So the solutions of the inequality x - 7 ≤ -10 are x ≤ -3.
To represent the numbers that are not solutions, we can negate the inequality and find the range that lies outside of x ≤ -3.
Step 2: Represent the numbers that are not solutions:
Negating x ≤ -3, we get x > -3.
Therefore, the inequality that represents the numbers that are not solutions of x - 7 ≤ -10 is x > -3.
To find the numbers that are not solutions of the inequality x-7 ≤ -10, we need to find the values of x that make the inequality false.
First, let's solve the inequality x-7 ≤ -10 to find the solutions:
x - 7 ≤ -10
To isolate x, add 7 to both sides:
x - 7 + 7 ≤ -10 + 7
x ≤ -3
So, the solutions to the inequality x-7 ≤ -10 are x ≤ -3.
To find the numbers that are not solutions, we need to consider all the values of x that make the inequality false. In this case, the numbers that are not solutions are the values of x that are greater than -3.
Therefore, the inequality that represents the numbers that are not solutions is x > -3.
your inequality is x-7 <= -10
so, you want everything that makes that statement false.
That is,
x-7 > -10
x > -3