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QuestionSelect all equations equivalent to f+g=5f+g=5 using properties of equality: f+g+4=7f+g+4=7, 11+f+g=1811+f+g=18, 8+f+g=148+f+g=14, 11+f+g=1611+f+g=16.

Studdy Solution

STEP 1

Assumptions1. The given equation is f+g=5f+g=5 . We are to find all equations that are equivalent to the given equation using properties of equality.

STEP 2

We will start with the first equation f+g+4=7f+g+4=7. We can use the subtraction property of equality to subtract4 from both sides of the equation to isolate f+gf+g.
f+g+4−4=7−4f+g+4-4=7-4

STEP 3

implify the left and right sides of the equation.
f+g=7−f+g=7-

STEP 4

Calculate the right side of the equation.
f+g=3f+g=3

STEP 5

The equation f+g=3f+g=3 is not equivalent to the given equation f+g=5f+g=5. So, the first equation is not an equivalent equation.

STEP 6

Now, let's move on to the second equation 11+f+g=1811+f+g=18. We can use the subtraction property of equality to subtract11 from both sides of the equation to isolate f+gf+g.
11+f+g−11=18−1111+f+g-11=18-11

STEP 7

implify the left and right sides of the equation.
f+g=18−11f+g=18-11

STEP 8

Calculate the right side of the equation.
f+g=7f+g=7

STEP 9

The equation f+g=7f+g=7 is not equivalent to the given equation f+g=5f+g=5. So, the second equation is not an equivalent equation.

STEP 10

Next, let's examine the third equation 8+f+g=148+f+g=14. We can use the subtraction property of equality to subtract8 from both sides of the equation to isolate f+gf+g.
8+f+g−8=14−88+f+g-8=14-8

STEP 11

implify the left and right sides of the equation.
f+g=14−8f+g=14-8

STEP 12

Calculate the right side of the equation.
f+g=6f+g=6

STEP 13

The equation f+g=6f+g=6 is not equivalent to the given equation f+g=5f+g=5. So, the third equation is not an equivalent equation.

STEP 14

Finally, let's look at the fourth equation 11+f+g=1611+f+g=16. We can use the subtraction property of equality to subtract11 from both sides of the equation to isolate f+gf+g.
11+f+g−11=16−1111+f+g-11=16-11

STEP 15

implify the left and right sides of the equation.
f+g=−11f+g=-11

STEP 16

Calculate the right side of the equation.
f+g=5f+g=5

STEP 17

The equation f+g=5f+g=5 is equivalent to the given equation f+g=5f+g=5. So, the fourth equation is an equivalent equation.
In conclusion, only the equation 11+f+g=1611+f+g=16 is equivalent to the given equation f+g=5f+g=5.

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