Question Solve the linear equation $\frac{2}{3}(x-7) = -2$ for the value of $x$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $\frac{2}{3}(x-7) = -2$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we need to isolate the term containing $x$ . To do this, we can multiply both sides of the equation by the reciprocal of $\frac{2}{3}$ , which is $\frac{3}{2}$ .
$\frac{3}{2} \cdot \frac{2}{3}(x-7) = \frac{3}{2} \cdot -2$

STEP 3

The $\frac{3}{2}$ and $\frac{2}{3}$ on the left side cancel each other out, leaving us with:
$(x-7) = \frac{3}{2} \cdot -2$

STEP 4

Now, calculate the right side of the equation:
$x - 7 = -3$

STEP 5

To solve for $x$ , we need to isolate it by adding 7 to both sides of the equation:
$x - 7 + 7 = -3 + 7$

STEP 6

Simplify both sides of the equation:
$x = 4$
The solution to the equation $\frac{2}{3}(x-7) = -2$ is $x = 4$ .

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Question Solve the linear equation $\frac{2}{3}(x-7) = -2$ for the value of $x$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $\frac{2}{3}(x-7) = -2$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we need to isolate the term containing $x$ . To do this, we can multiply both sides of the equation by the reciprocal of $\frac{2}{3}$ , which is $\frac{3}{2}$ .
$\frac{3}{2} \cdot \frac{2}{3}(x-7) = \frac{3}{2} \cdot -2$

STEP 3

The $\frac{3}{2}$ and $\frac{2}{3}$ on the left side cancel each other out, leaving us with:
$(x-7) = \frac{3}{2} \cdot -2$

STEP 4

Now, calculate the right side of the equation:
$x - 7 = -3$

STEP 5

To solve for $x$ , we need to isolate it by adding 7 to both sides of the equation:
$x - 7 + 7 = -3 + 7$

STEP 6

Simplify both sides of the equation:
$x = 4$
The solution to the equation $\frac{2}{3}(x-7) = -2$ is $x = 4$ .

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Question Solve the linear equation 23(x−7)=−2\frac{2}{3}(x-7) = -232​(x−7)=−2 for the value of xxx.

Studdy Solution

STEP 1

Assumptions1. We are given the equation 23(x−7)=−2\frac{2}{3}(x-7) = -232​(x−7)=−2.2. We need to solve for the variable xxx.

STEP 2

First, we need to isolate the term containing xxx. To do this, we can multiply both sides of the equation by the reciprocal of 23\frac{2}{3}32​, which is 32\frac{3}{2}23​.32⋅23(x−7)=32⋅−2\frac{3}{2} \cdot \frac{2}{3}(x-7) = \frac{3}{2} \cdot -223​⋅32​(x−7)=23​⋅−2

STEP 3

The 32\frac{3}{2}23​ and 23\frac{2}{3}32​ on the left side cancel each other out, leaving us with:(x−7)=32⋅−2(x-7) = \frac{3}{2} \cdot -2(x−7)=23​⋅−2

STEP 4

Now, calculate the right side of the equation:x−7=−3x - 7 = -3x−7=−3

STEP 5

To solve for xxx, we need to isolate it by adding 7 to both sides of the equation:x−7+7=−3+7x - 7 + 7 = -3 + 7x−7+7=−3+7

STEP 6

Simplify both sides of the equation:x=4x = 4x=4The solution to the equation 23(x−7)=−2\frac{2}{3}(x-7) = -232​(x−7)=−2 is x=4x = 4x=4.

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Question Solve the linear equation $\frac{2}{3}(x-7) = -2$ for the value of $x$ .

Assumptions
1. We are given the equation $\frac{2}{3}(x-7) = -2$ .
2. We need to solve for the variable $x$ .

First, we need to isolate the term containing $x$ . To do this, we can multiply both sides of the equation by the reciprocal of $\frac{2}{3}$ , which is $\frac{3}{2}$ .
$\frac{3}{2} \cdot \frac{2}{3}(x-7) = \frac{3}{2} \cdot -2$

The $\frac{3}{2}$ and $\frac{2}{3}$ on the left side cancel each other out, leaving us with:
$(x-7) = \frac{3}{2} \cdot -2$

Now, calculate the right side of the equation:
$x - 7 = -3$

To solve for $x$ , we need to isolate it by adding 7 to both sides of the equation:
$x - 7 + 7 = -3 + 7$

Simplify both sides of the equation:
$x = 4$
The solution to the equation $\frac{2}{3}(x-7) = -2$ is $x = 4$ .