Math

QuestionIdentify equivalent equations to 54z=7054-z=70 using properties of equality from the options provided.

Studdy Solution

STEP 1

Assumptions1. The original equation is 54z=7054-z=70 . We are looking for equivalent equations, meaning they should have the same solution as the original equation3. The properties of equality allow us to perform the same operation on both sides of an equation without changing the solution

STEP 2

First, let's solve the original equation for zz.
54z=7054-z=70

STEP 3

Subtract54 from both sides of the equation to isolate z-z on one side.
z=7054-z =70 -54

STEP 4

Calculate the right side of the equation.
z=16-z =16

STEP 5

Multiply both sides of the equation by -1 to solve for zz.
z=16z = -16

STEP 6

Now that we have the solution for zz, we can substitute zz into each of the given equations to see if they are equivalent to the original equation.

STEP 7

Substitute zz into the first equation.
54(16)5=12\frac{54-(-16)}{5}=12

STEP 8

implify the numerator.
705=12\frac{70}{5}=12

STEP 9

Calculate the left side of the equation.
14=1214=12This equation is not equivalent to the original equation.

STEP 10

Substitute zz into the second equation.
54(16)5=14\frac{54-(-16)}{5}=14

STEP 11

implify the numerator.
705=14\frac{70}{5}=14

STEP 12

Calculate the left side of the equation.
14=1414=14This equation is equivalent to the original equation.

STEP 13

Substitute zz into the third equation.
54(16)=7\frac{54-(-16)}{}=7

STEP 14

implify the numerator.
7014=7\frac{70}{14}=7

STEP 15

Calculate the left side of the equation.
5=75=7This equation is not equivalent to the original equation.

STEP 16

Substitute zz into the fourth equation.
54(16)=11\frac{54-(-16)}{}=11

STEP 17

implify the numerator.
707=11\frac{70}{7}=11

STEP 18

Calculate the left side of the equation.
10=1110=11This equation is not equivalent to the original equation.
The only equivalent equation to 54z=7054-z=70 is 54z5=14\frac{54-z}{5}=14.

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