How can mental math help you find solutions to inequalities?

There are many examples the basics are also easy to remember.

Step-by-step explanation:

We can input these for the following equation.

x > 5

(x is greater than 5)

Then compare to - x < 5

(minus x is less than 5)

We try a sum

3x -2 ≤ 1

we can then balance subtract -2

3x ≤ -1

then divide by 3

x= -1 /3

We try another value

3x -2 ≤ 0

1 ≤ 3x

1/3 ≥ x

We can check that each equality fits and alter the number accordingly.

For the first one we are saying it is no greater than 1

For the second we say it is greater than zero.

We are able to prove both have the answer.

Just like when we look for negative percentages and count down we record this as we count in mental math.

answer:

(-8,7)

explanation:

we know that  

f

(

−

3

)

=

7

therefore, if we wish to get the output as 7, in the function, we need to have our input to be -3.

looking at the function  

f

(

x

+

5

)

, what should the value of x be, such that the input in the function becomes 7?

we simply equate the terms,

x

+

5

=

−

3

x

=

−

8

thus, the point on the new function would be  

(

−

8

,

7

)

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: