Math

QuestionSelect equations equivalent to 12=5j12=5 j using properties of equality: 19=7+5j19=7+5 j, 16=5j+416=5 j+4, 15=5j+315=5 j+3, 17=5+5j17=5+5 j.

Studdy Solution

STEP 1

Assumptions1. We are given the equation 12=5j12=5j. . We need to find all the equations that are equivalent to the given equation.
3. The properties of equality are valid.

STEP 2

First, let's solve the given equation for jj.
j=125j = \frac{12}{5}

STEP 3

Now, let's substitute jj into the first equation to check if it's equivalent to the given equation.
19=7+5j19 =7 +5jSubstitute j=125j = \frac{12}{5} into the equation.
19=7+5(125)19 =7 +5 \left(\frac{12}{5}\right)

STEP 4

implify the equation.
19=7+1219 =7 +12

STEP 5

Calculate the right side of the equation.
19=1919 =19The first equation is equivalent to the given equation.

STEP 6

Repeat the process for the second equation.
16=5j+416 =5j +4Substitute j=125j = \frac{12}{5} into the equation.
16=5(125)+416 =5 \left(\frac{12}{5}\right) +4

STEP 7

implify the equation.
16=12+416 =12 +4

STEP 8

Calculate the right side of the equation.
16=1616 =16The second equation is equivalent to the given equation.

STEP 9

Repeat the process for the third equation.
15=5j+315 =5j +3Substitute j=125j = \frac{12}{5} into the equation.
15=5(125)+315 =5 \left(\frac{12}{5}\right) +3

STEP 10

implify the equation.
15=12+315 =12 +3

STEP 11

Calculate the right side of the equation.
15=1515 =15The third equation is equivalent to the given equation.

STEP 12

Repeat the process for the fourth equation.
17=5+5j17 =5 +5jSubstitute j=125j = \frac{12}{5} into the equation.
17=5+5(125)17 =5 +5 \left(\frac{12}{5}\right)

STEP 13

implify the equation.
17=5+1217 =5 +12

STEP 14

Calculate the right side of the equation.
17=1717 =17The fourth equation is equivalent to the given equation.
So, all the given equations are equivalent to the original equation 12=j12=j.

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