Solved on Dec 11, 2023

Find the equations equivalent to $n-11=8$ using properties of equality.

STEP 1

Assumptions
1. We are given the equation $n - 11 = 8$ .
2. We need to determine which of the following equations are equivalent to the given equation using properties of equality: a. $n - 2 = 8 + 9$ b. $3 + n - 11 = 11$ c. $n - 11 + 7 = 13$ d. $10 + n - 11 = 18$
3. Properties of equality include the addition property of equality (if $a = b$ , then $a + c = b + c$ ) and the subtraction property of equality (if $a = b$ , then $a - c = b - c$ ).

STEP 2

First, we will solve the given equation for $n$ .
$n - 11 = 8$

STEP 3

Add 11 to both sides of the equation to isolate $n$ .
$n - 11 + 11 = 8 + 11$

STEP 4

Simplify both sides of the equation.
$n = 19$

STEP 5

Now that we have the value of $n$ , we can check each of the provided equations to see if they are equivalent by substituting $n = 19$ and using properties of equality.

STEP 6

Check the first equation $n - 2 = 8 + 9$ .
$19 - 2 = 8 + 9$

STEP 7

Simplify both sides of the equation.
$17 = 17$
Since both sides are equal, the first equation is equivalent to the given equation.

STEP 8

Check the second equation $3 + n - 11 = 11$ .
$3 + 19 - 11 = 11$

STEP 9

Simplify both sides of the equation.
$11 = 11$
Since both sides are equal, the second equation is equivalent to the given equation.

STEP 10

Check the third equation $n - 11 + 7 = 13$ .
$19 - 11 + 7 = 13$

STEP 11

Simplify both sides of the equation.
$15 = 13$
Since both sides are not equal, the third equation is not equivalent to the given equation.

STEP 12

Check the fourth equation $10 + n - 11 = 18$ .
$10 + 19 - 11 = 18$

STEP 13

Simplify both sides of the equation.
$18 = 18$
Since both sides are equal, the fourth equation is equivalent to the given equation.

STEP 14

Conclude which equations are equivalent to the given equation $n - 11 = 8$ .
The equivalent equations are:
- $n - 2 = 8 + 9$ - $3 + n - 11 = 11$ - $10 + n - 11 = 18$
The equation $n - 11 + 7 = 13$ is not equivalent.

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Find the equations equivalent to $n-11=8$ using properties of equality.

STEP 1

STEP 2

First, we will solve the given equation for $n$ .
$n - 11 = 8$

STEP 3

Add 11 to both sides of the equation to isolate $n$ .
$n - 11 + 11 = 8 + 11$

STEP 4

Simplify both sides of the equation.
$n = 19$

STEP 5

Now that we have the value of $n$ , we can check each of the provided equations to see if they are equivalent by substituting $n = 19$ and using properties of equality.

STEP 6

Check the first equation $n - 2 = 8 + 9$ .
$19 - 2 = 8 + 9$

STEP 7

Simplify both sides of the equation.
$17 = 17$
Since both sides are equal, the first equation is equivalent to the given equation.

STEP 8

Check the second equation $3 + n - 11 = 11$ .
$3 + 19 - 11 = 11$

STEP 9

Simplify both sides of the equation.
$11 = 11$
Since both sides are equal, the second equation is equivalent to the given equation.

STEP 10

Check the third equation $n - 11 + 7 = 13$ .
$19 - 11 + 7 = 13$

STEP 11

Simplify both sides of the equation.
$15 = 13$
Since both sides are not equal, the third equation is not equivalent to the given equation.

STEP 12

Check the fourth equation $10 + n - 11 = 18$ .
$10 + 19 - 11 = 18$

STEP 13

Simplify both sides of the equation.
$18 = 18$
Since both sides are equal, the fourth equation is equivalent to the given equation.

STEP 14

Conclude which equations are equivalent to the given equation $n - 11 = 8$ .
The equivalent equations are:
- $n - 2 = 8 + 9$ - $3 + n - 11 = 11$ - $10 + n - 11 = 18$
The equation $n - 11 + 7 = 13$ is not equivalent.

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Find the equations equivalent to n−11=8n-11=8n−11=8 using properties of equality.

STEP 1

STEP 2

First, we will solve the given equation for n n n.n−11=8 n - 11 = 8 n−11=8

STEP 3

Add 11 to both sides of the equation to isolate n n n.n−11+11=8+11 n - 11 + 11 = 8 + 11 n−11+11=8+11

STEP 4

Simplify both sides of the equation.n=19 n = 19 n=19

STEP 5

Now that we have the value of n n n, we can check each of the provided equations to see if they are equivalent by substituting n=19 n = 19 n=19 and using properties of equality.

STEP 6

Check the first equation n−2=8+9 n - 2 = 8 + 9 n−2=8+9.19−2=8+9 19 - 2 = 8 + 9 19−2=8+9

STEP 7

Simplify both sides of the equation.17=17 17 = 17 17=17Since both sides are equal, the first equation is equivalent to the given equation.

STEP 8

Check the second equation 3+n−11=11 3 + n - 11 = 11 3+n−11=11.3+19−11=11 3 + 19 - 11 = 11 3+19−11=11

STEP 9

Simplify both sides of the equation.11=11 11 = 11 11=11Since both sides are equal, the second equation is equivalent to the given equation.

STEP 10

Check the third equation n−11+7=13 n - 11 + 7 = 13 n−11+7=13.19−11+7=13 19 - 11 + 7 = 13 19−11+7=13

STEP 11

Simplify both sides of the equation.15=13 15 = 13 15=13Since both sides are not equal, the third equation is not equivalent to the given equation.

STEP 12

Check the fourth equation 10+n−11=18 10 + n - 11 = 18 10+n−11=18.10+19−11=18 10 + 19 - 11 = 18 10+19−11=18

STEP 13

Simplify both sides of the equation.18=18 18 = 18 18=18Since both sides are equal, the fourth equation is equivalent to the given equation.

STEP 14

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Find the equations equivalent to $n-11=8$ using properties of equality.

First, we will solve the given equation for $n$ .
$n - 11 = 8$

Add 11 to both sides of the equation to isolate $n$ .
$n - 11 + 11 = 8 + 11$

Simplify both sides of the equation.
$n = 19$

Now that we have the value of $n$ , we can check each of the provided equations to see if they are equivalent by substituting $n = 19$ and using properties of equality.

Check the first equation $n - 2 = 8 + 9$ .
$19 - 2 = 8 + 9$

Simplify both sides of the equation.
$17 = 17$
Since both sides are equal, the first equation is equivalent to the given equation.

Check the second equation $3 + n - 11 = 11$ .
$3 + 19 - 11 = 11$

Simplify both sides of the equation.
$11 = 11$
Since both sides are equal, the second equation is equivalent to the given equation.

Check the third equation $n - 11 + 7 = 13$ .
$19 - 11 + 7 = 13$

Simplify both sides of the equation.
$15 = 13$
Since both sides are not equal, the third equation is not equivalent to the given equation.

Check the fourth equation $10 + n - 11 = 18$ .
$10 + 19 - 11 = 18$

Simplify both sides of the equation.
$18 = 18$
Since both sides are equal, the fourth equation is equivalent to the given equation.