Solved on Jan 24, 2024

Solve the equation $x-2=10$ using the addition or subtraction property of equality, then check the solution.

STEP 1

Assumptions
1. We are given the equation $x - 2 = 10$ .
2. We will use the addition property of equality to solve for $x$ .
3. To check the solution, we will substitute the value of $x$ back into the original equation.

STEP 2

To isolate the variable $x$ on one side of the equation, we need to eliminate the $-2$ from the left side. We can do this by adding $2$ to both sides of the equation, which is an application of the addition property of equality.
$x - 2 + 2 = 10 + 2$

STEP 3

Perform the addition on both sides of the equation.
$x = 12$

STEP 4

Now we have the value of $x$ , but we must check our solution to ensure it is correct. We do this by substituting $x = 12$ back into the original equation.
$12 - 2 \stackrel{?}{=} 10$

STEP 5

Perform the subtraction on the left side of the equation to see if it equals the right side.
$10 = 10$

STEP 6

Since both sides of the equation are equal after the substitution, our solution $x = 12$ is correct.
The solution set is $\{12\}$ .

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Solve the equation $x-2=10$ using the addition or subtraction property of equality, then check the solution.

STEP 1

Assumptions
1. We are given the equation $x - 2 = 10$ .
2. We will use the addition property of equality to solve for $x$ .
3. To check the solution, we will substitute the value of $x$ back into the original equation.

STEP 2

To isolate the variable $x$ on one side of the equation, we need to eliminate the $-2$ from the left side. We can do this by adding $2$ to both sides of the equation, which is an application of the addition property of equality.
$x - 2 + 2 = 10 + 2$

STEP 3

Perform the addition on both sides of the equation.
$x = 12$

STEP 4

Now we have the value of $x$ , but we must check our solution to ensure it is correct. We do this by substituting $x = 12$ back into the original equation.
$12 - 2 \stackrel{?}{=} 10$

STEP 5

Perform the subtraction on the left side of the equation to see if it equals the right side.
$10 = 10$

STEP 6

Since both sides of the equation are equal after the substitution, our solution $x = 12$ is correct.
The solution set is $\{12\}$ .

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Solve the equation x−2=10x-2=10x−2=10 using the addition or subtraction property of equality, then check the solution.

STEP 1

Assumptions1. We are given the equation x−2=10x - 2 = 10x−2=10.2. We will use the addition property of equality to solve for xxx.3. To check the solution, we will substitute the value of xxx back into the original equation.

STEP 2

To isolate the variable xxx on one side of the equation, we need to eliminate the −2-2−2 from the left side. We can do this by adding 222 to both sides of the equation, which is an application of the addition property of equality.x−2+2=10+2x - 2 + 2 = 10 + 2x−2+2=10+2

STEP 3

Perform the addition on both sides of the equation.x=12x = 12x=12

STEP 4

Now we have the value of xxx, but we must check our solution to ensure it is correct. We do this by substituting x=12x = 12x=12 back into the original equation.12−2=?1012 - 2 \stackrel{?}{=} 1012−2=?10

STEP 5

Perform the subtraction on the left side of the equation to see if it equals the right side.10=1010 = 1010=10

STEP 6

Since both sides of the equation are equal after the substitution, our solution x=12x = 12x=12 is correct.The solution set is {12}\{12\}{12}.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the equation $x-2=10$ using the addition or subtraction property of equality, then check the solution.

Assumptions
1. We are given the equation $x - 2 = 10$ .
2. We will use the addition property of equality to solve for $x$ .
3. To check the solution, we will substitute the value of $x$ back into the original equation.

To isolate the variable $x$ on one side of the equation, we need to eliminate the $-2$ from the left side. We can do this by adding $2$ to both sides of the equation, which is an application of the addition property of equality.
$x - 2 + 2 = 10 + 2$

Perform the addition on both sides of the equation.
$x = 12$

Now we have the value of $x$ , but we must check our solution to ensure it is correct. We do this by substituting $x = 12$ back into the original equation.
$12 - 2 \stackrel{?}{=} 10$

Perform the subtraction on the left side of the equation to see if it equals the right side.
$10 = 10$

Since both sides of the equation are equal after the substitution, our solution $x = 12$ is correct.
The solution set is $\{12\}$ .