Which property of real numbers is illustrated by the equation?

9514 1404 393

  additive inverse

Step-by-step explanation:

The equation shows that the sum of a number and its additive inverse is zero. This is the additive inverse property.

Additional comments

This property is used, together with the identity property of addition, to solve equations by making terms disappear where you don't want them.

Example:

  x + 1 = 3

We would like to remove the +1 in order to find the value of x. Using the additive inverse property, we add the additive inverse of +1 to both sides of the equation.

  x +1 -1 = 3 -1

The additive inverse property tells us the sum of +1 and -1 is zero, so this becomes ...

  x +0 = 2

The additive identity property tells us the sum of x and 0 is simply x, so ...

  x = 2

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is