Question Solve the equation $7z - 23 = z + 7$ using addition and multiplication properties of equality, then check the solution.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $7z - 23 = z + 7$ .
2. We will use the addition property of equality to isolate terms with the variable $z$ on one side of the equation.
3. We will use the multiplication property of equality to solve for $z$ .
4. We will check the proposed solution by substituting it back into the original equation.

STEP 2

First, we will use the addition property of equality to get all the $z$ terms on one side of the equation. We do this by subtracting $z$ from both sides of the equation.
$7z - 23 - z = z + 7 - z$

STEP 3

Simplify both sides of the equation by combining like terms.
$6z - 23 = 7$

STEP 4

Next, we will use the addition property of equality again to isolate the $z$ term by adding $23$ to both sides of the equation.
$6z - 23 + 23 = 7 + 23$

STEP 5

Simplify both sides of the equation.
$6z = 30$

STEP 6

Now we will use the multiplication property of equality to solve for $z$ by dividing both sides of the equation by $6$ .
$\frac{6z}{6} = \frac{30}{6}$

STEP 7

Simplify both sides of the equation to find the value of $z$ .
$z = 5$

STEP 8

We have proposed that the solution is $z = 5$ . Now we will check this solution by substituting it back into the original equation.
$7(5) - 23 = 5 + 7$

STEP 9

Perform the multiplication and addition to check if both sides of the equation are equal.
$35 - 23 = 12$

STEP 10

Simplify both sides of the equation.
$12 = 12$

STEP 11

Since both sides of the equation are equal, our proposed solution $z = 5$ is correct.
The solution to the equation $7z - 23 = z + 7$ is $z = 5$ .

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Question Solve the equation $7z - 23 = z + 7$ using addition and multiplication properties of equality, then check the solution.

Studdy Solution

STEP 1

STEP 2

First, we will use the addition property of equality to get all the $z$ terms on one side of the equation. We do this by subtracting $z$ from both sides of the equation.
$7z - 23 - z = z + 7 - z$

STEP 3

Simplify both sides of the equation by combining like terms.
$6z - 23 = 7$

STEP 4

Next, we will use the addition property of equality again to isolate the $z$ term by adding $23$ to both sides of the equation.
$6z - 23 + 23 = 7 + 23$

STEP 5

Simplify both sides of the equation.
$6z = 30$

STEP 6

Now we will use the multiplication property of equality to solve for $z$ by dividing both sides of the equation by $6$ .
$\frac{6z}{6} = \frac{30}{6}$

STEP 7

Simplify both sides of the equation to find the value of $z$ .
$z = 5$

STEP 8

We have proposed that the solution is $z = 5$ . Now we will check this solution by substituting it back into the original equation.
$7(5) - 23 = 5 + 7$

STEP 9

Perform the multiplication and addition to check if both sides of the equation are equal.
$35 - 23 = 12$

STEP 10

Simplify both sides of the equation.
$12 = 12$

STEP 11

Since both sides of the equation are equal, our proposed solution $z = 5$ is correct.
The solution to the equation $7z - 23 = z + 7$ is $z = 5$ .

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Question Solve the equation 7z−23=z+77z - 23 = z + 77z−23=z+7 using addition and multiplication properties of equality, then check the solution.

Studdy Solution

STEP 1

STEP 2

First, we will use the addition property of equality to get all the zzz terms on one side of the equation. We do this by subtracting zzz from both sides of the equation.7z−23−z=z+7−z7z - 23 - z = z + 7 - z7z−23−z=z+7−z

STEP 3

Simplify both sides of the equation by combining like terms.6z−23=76z - 23 = 76z−23=7

STEP 4

Next, we will use the addition property of equality again to isolate the zzz term by adding 232323 to both sides of the equation.6z−23+23=7+236z - 23 + 23 = 7 + 236z−23+23=7+23

STEP 5

Simplify both sides of the equation.6z=306z = 306z=30

STEP 6

Now we will use the multiplication property of equality to solve for zzz by dividing both sides of the equation by 666.6z6=306\frac{6z}{6} = \frac{30}{6}66z​=630​

STEP 7

Simplify both sides of the equation to find the value of zzz.z=5z = 5z=5

STEP 8

We have proposed that the solution is z=5z = 5z=5. Now we will check this solution by substituting it back into the original equation.7(5)−23=5+77(5) - 23 = 5 + 77(5)−23=5+7

STEP 9

Perform the multiplication and addition to check if both sides of the equation are equal.35−23=1235 - 23 = 1235−23=12

STEP 10

Simplify both sides of the equation.12=1212 = 1212=12

STEP 11

Since both sides of the equation are equal, our proposed solution z=5z = 5z=5 is correct.The solution to the equation 7z−23=z+77z - 23 = z + 77z−23=z+7 is z=5z = 5z=5.

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Question Solve the equation $7z - 23 = z + 7$ using addition and multiplication properties of equality, then check the solution.

First, we will use the addition property of equality to get all the $z$ terms on one side of the equation. We do this by subtracting $z$ from both sides of the equation.
$7z - 23 - z = z + 7 - z$

Simplify both sides of the equation by combining like terms.
$6z - 23 = 7$

Next, we will use the addition property of equality again to isolate the $z$ term by adding $23$ to both sides of the equation.
$6z - 23 + 23 = 7 + 23$

Simplify both sides of the equation.
$6z = 30$

Now we will use the multiplication property of equality to solve for $z$ by dividing both sides of the equation by $6$ .
$\frac{6z}{6} = \frac{30}{6}$

Simplify both sides of the equation to find the value of $z$ .
$z = 5$

We have proposed that the solution is $z = 5$ . Now we will check this solution by substituting it back into the original equation.
$7(5) - 23 = 5 + 7$

Perform the multiplication and addition to check if both sides of the equation are equal.
$35 - 23 = 12$

Simplify both sides of the equation.
$12 = 12$

Since both sides of the equation are equal, our proposed solution $z = 5$ is correct.
The solution to the equation $7z - 23 = z + 7$ is $z = 5$ .