Solved on Feb 06, 2024

Solve for $z$ in the equation $5(z+2)=15$ .

STEP 1

Assumptions
1. We are given the equation $5(z+2)=15$ .
2. We need to solve for the variable $z$ .

STEP 2

First, we need to distribute the 5 across the terms inside the parentheses.
$5(z+2) = 5z + 5 \cdot 2$

STEP 3

Perform the multiplication to simplify the left side of the equation.
$5z + 5 \cdot 2 = 5z + 10$

STEP 4

Now, rewrite the equation with the simplified left side.
$5z + 10 = 15$

STEP 5

To solve for $z$ , we need to isolate $z$ on one side of the equation. We can start by subtracting 10 from both sides of the equation to move the constant term to the right side.
$5z + 10 - 10 = 15 - 10$

STEP 6

Simplify both sides of the equation after subtraction.
$5z = 5$

STEP 7

Now, divide both sides of the equation by 5 to solve for $z$ .
$\frac{5z}{5} = \frac{5}{5}$

STEP 8

Simplify both sides of the equation after division.
$z = 1$
The solution to the equation $5(z+2)=15$ is $z=1$ .

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Solve for $z$ in the equation $5(z+2)=15$ .

STEP 1

Assumptions
1. We are given the equation $5(z+2)=15$ .
2. We need to solve for the variable $z$ .

STEP 2

First, we need to distribute the 5 across the terms inside the parentheses.
$5(z+2) = 5z + 5 \cdot 2$

STEP 3

Perform the multiplication to simplify the left side of the equation.
$5z + 5 \cdot 2 = 5z + 10$

STEP 4

Now, rewrite the equation with the simplified left side.
$5z + 10 = 15$

STEP 5

To solve for $z$ , we need to isolate $z$ on one side of the equation. We can start by subtracting 10 from both sides of the equation to move the constant term to the right side.
$5z + 10 - 10 = 15 - 10$

STEP 6

Simplify both sides of the equation after subtraction.
$5z = 5$

STEP 7

Now, divide both sides of the equation by 5 to solve for $z$ .
$\frac{5z}{5} = \frac{5}{5}$

STEP 8

Simplify both sides of the equation after division.
$z = 1$
The solution to the equation $5(z+2)=15$ is $z=1$ .

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Solve for zzz in the equation 5(z+2)=155(z+2)=155(z+2)=15.

STEP 1

Assumptions1. We are given the equation 5(z+2)=155(z+2)=155(z+2)=15.2. We need to solve for the variable zzz.

STEP 2

First, we need to distribute the 5 across the terms inside the parentheses.5(z+2)=5z+5⋅25(z+2) = 5z + 5 \cdot 25(z+2)=5z+5⋅2

STEP 3

Perform the multiplication to simplify the left side of the equation.5z+5⋅2=5z+105z + 5 \cdot 2 = 5z + 105z+5⋅2=5z+10

STEP 4

Now, rewrite the equation with the simplified left side.5z+10=155z + 10 = 155z+10=15

STEP 5

To solve for zzz, we need to isolate zzz on one side of the equation. We can start by subtracting 10 from both sides of the equation to move the constant term to the right side.5z+10−10=15−105z + 10 - 10 = 15 - 105z+10−10=15−10

STEP 6

Simplify both sides of the equation after subtraction.5z=55z = 55z=5

STEP 7

Now, divide both sides of the equation by 5 to solve for zzz.5z5=55\frac{5z}{5} = \frac{5}{5}55z​=55​

STEP 8

Simplify both sides of the equation after division.z=1z = 1z=1The solution to the equation 5(z+2)=155(z+2)=155(z+2)=15 is z=1z=1z=1.

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Solve for $z$ in the equation $5(z+2)=15$ .

Assumptions
1. We are given the equation $5(z+2)=15$ .
2. We need to solve for the variable $z$ .

First, we need to distribute the 5 across the terms inside the parentheses.
$5(z+2) = 5z + 5 \cdot 2$

Perform the multiplication to simplify the left side of the equation.
$5z + 5 \cdot 2 = 5z + 10$

Now, rewrite the equation with the simplified left side.
$5z + 10 = 15$

To solve for $z$ , we need to isolate $z$ on one side of the equation. We can start by subtracting 10 from both sides of the equation to move the constant term to the right side.
$5z + 10 - 10 = 15 - 10$

Simplify both sides of the equation after subtraction.
$5z = 5$

Now, divide both sides of the equation by 5 to solve for $z$ .
$\frac{5z}{5} = \frac{5}{5}$

Simplify both sides of the equation after division.
$z = 1$
The solution to the equation $5(z+2)=15$ is $z=1$ .