Write an equation for each translation of y=|x|. 2.5 units left y = | x | – 2.5
y = | x | + 2.5
y = | x + 2.5 |
y = | x – 2.5 |

For this case we have that the main function is given by:

We want to move the function 2.5 units to the left.

For this, we follow the following rule:

Therefore, according to the rule we have:

The equation of the translated function is given by:

Option C

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3