QuestionSolve for $x$ in the equation $\frac{1}{2} x - 2 = \frac{1}{5}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the equation $\frac{1}{} x - = \frac{1}{5}$ . . We are to solve for $x$ .

STEP 2

First, we want to isolate the term with $x$ on one side of the equation. To do this, we add2 to both sides of the equation to cancel out the -2 on the left side.
$\frac{1}{2} x -2 +2 = \frac{1}{5} +2$

STEP 3

implify both sides of the equation.
$\frac{1}{2} x = \frac{1}{5} +2$

STEP 4

Convert the2 on the right side of the equation to a fraction with a denominator of to make addition easier.
$\frac{1}{2} x = \frac{1}{} + \frac{10}{}$

STEP 5

Add the fractions on the right side of the equation.
$\frac{1}{2} x = \frac{11}{5}$

STEP 6

Now, to solve for $x$ , we multiply both sides of the equation by2 to cancel out the $\frac{1}{2}$ on the left side.
$2 \cdot \frac{1}{2} x =2 \cdot \frac{11}{5}$

STEP 7

implify both sides of the equation.
$x = \frac{22}{5}$ So, the solution to the equation $\frac{1}{2} x -2 = \frac{1}{5}$ is $x = \frac{22}{5}$ .

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QuestionSolve for $x$ in the equation $\frac{1}{2} x - 2 = \frac{1}{5}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the equation $\frac{1}{} x - = \frac{1}{5}$ . . We are to solve for $x$ .

STEP 2

First, we want to isolate the term with $x$ on one side of the equation. To do this, we add2 to both sides of the equation to cancel out the -2 on the left side.
$\frac{1}{2} x -2 +2 = \frac{1}{5} +2$

STEP 3

implify both sides of the equation.
$\frac{1}{2} x = \frac{1}{5} +2$

STEP 4

Convert the2 on the right side of the equation to a fraction with a denominator of to make addition easier.
$\frac{1}{2} x = \frac{1}{} + \frac{10}{}$

STEP 5

Add the fractions on the right side of the equation.
$\frac{1}{2} x = \frac{11}{5}$

STEP 6

Now, to solve for $x$ , we multiply both sides of the equation by2 to cancel out the $\frac{1}{2}$ on the left side.
$2 \cdot \frac{1}{2} x =2 \cdot \frac{11}{5}$

STEP 7

implify both sides of the equation.
$x = \frac{22}{5}$ So, the solution to the equation $\frac{1}{2} x -2 = \frac{1}{5}$ is $x = \frac{22}{5}$ .

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QuestionSolve for xxx in the equation 12x−2=15\frac{1}{2} x - 2 = \frac{1}{5}21​x−2=51​.

Studdy Solution

STEP 1

Assumptions1. We are given the equation 1x−=15\frac{1}{} x - = \frac{1}{5}1​x−=51​. . We are to solve for xxx.

STEP 2

First, we want to isolate the term with xxx on one side of the equation. To do this, we add2 to both sides of the equation to cancel out the -2 on the left side.12x−2+2=15+2\frac{1}{2} x -2 +2 = \frac{1}{5} +221​x−2+2=51​+2

STEP 3

implify both sides of the equation.12x=15+2\frac{1}{2} x = \frac{1}{5} +221​x=51​+2

STEP 4

Convert the2 on the right side of the equation to a fraction with a denominator of to make addition easier.12x=1+10\frac{1}{2} x = \frac{1}{} + \frac{10}{}21​x=1​+10​

STEP 5

Add the fractions on the right side of the equation.12x=115\frac{1}{2} x = \frac{11}{5}21​x=511​

STEP 6

Now, to solve for xxx, we multiply both sides of the equation by2 to cancel out the 12\frac{1}{2}21​ on the left side.2⋅12x=2⋅1152 \cdot \frac{1}{2} x =2 \cdot \frac{11}{5}2⋅21​x=2⋅511​

STEP 7

implify both sides of the equation.x=225x = \frac{22}{5}x=522​So, the solution to the equation 12x−2=15\frac{1}{2} x -2 = \frac{1}{5}21​x−2=51​ is x=225x = \frac{22}{5}x=522​.

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QuestionSolve for $x$ in the equation $\frac{1}{2} x - 2 = \frac{1}{5}$ .

Assumptions1. We are given the equation $\frac{1}{} x - = \frac{1}{5}$ . . We are to solve for $x$ .

First, we want to isolate the term with $x$ on one side of the equation. To do this, we add2 to both sides of the equation to cancel out the -2 on the left side.
$\frac{1}{2} x -2 +2 = \frac{1}{5} +2$

implify both sides of the equation.
$\frac{1}{2} x = \frac{1}{5} +2$

Convert the2 on the right side of the equation to a fraction with a denominator of to make addition easier.
$\frac{1}{2} x = \frac{1}{} + \frac{10}{}$

Add the fractions on the right side of the equation.
$\frac{1}{2} x = \frac{11}{5}$

Now, to solve for $x$ , we multiply both sides of the equation by2 to cancel out the $\frac{1}{2}$ on the left side.
$2 \cdot \frac{1}{2} x =2 \cdot \frac{11}{5}$

implify both sides of the equation.
$x = \frac{22}{5}$ So, the solution to the equation $\frac{1}{2} x -2 = \frac{1}{5}$ is $x = \frac{22}{5}$ .