Solved on Jan 23, 2024

Solve the equation $\frac{3}{7} x + 5 = 8$ to find the value of $x$ .

STEP 1

Assumptions
1. We are given the linear equation $\frac{3}{7} x + 5 = 8$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we want to isolate the term containing $x$ on one side of the equation. We can do this by subtracting 5 from both sides of the equation.
$\frac{3}{7} x + 5 - 5 = 8 - 5$

STEP 3

Perform the subtraction on both sides of the equation.
$\frac{3}{7} x = 3$

STEP 4

Now, we need to solve for $x$ by getting rid of the fraction. We can do this by multiplying both sides of the equation by the reciprocal of $\frac{3}{7}$ , which is $\frac{7}{3}$ .
$\frac{7}{3} \cdot \frac{3}{7} x = 3 \cdot \frac{7}{3}$

STEP 5

Simplify both sides of the equation. On the left side, the $\frac{7}{3}$ and $\frac{3}{7}$ will cancel each other out, leaving us with $x$ . On the right side, we multiply 3 by $\frac{7}{3}$ .
$x = 3 \cdot \frac{7}{3}$

STEP 6

Perform the multiplication on the right side of the equation.
$x = \frac{3 \cdot 7}{3}$

STEP 7

Cancel the common factor of 3 in the numerator and the denominator.
$x = \frac{7}{1}$

STEP 8

Simplify the fraction to find the value of $x$ .
$x = 7$
The solution to the equation $\frac{3}{7} x + 5 = 8$ is $x = 7$ .

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Solve the equation $\frac{3}{7} x + 5 = 8$ to find the value of $x$ .

STEP 1

Assumptions
1. We are given the linear equation $\frac{3}{7} x + 5 = 8$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we want to isolate the term containing $x$ on one side of the equation. We can do this by subtracting 5 from both sides of the equation.
$\frac{3}{7} x + 5 - 5 = 8 - 5$

STEP 3

Perform the subtraction on both sides of the equation.
$\frac{3}{7} x = 3$

STEP 4

Now, we need to solve for $x$ by getting rid of the fraction. We can do this by multiplying both sides of the equation by the reciprocal of $\frac{3}{7}$ , which is $\frac{7}{3}$ .
$\frac{7}{3} \cdot \frac{3}{7} x = 3 \cdot \frac{7}{3}$

STEP 5

Simplify both sides of the equation. On the left side, the $\frac{7}{3}$ and $\frac{3}{7}$ will cancel each other out, leaving us with $x$ . On the right side, we multiply 3 by $\frac{7}{3}$ .
$x = 3 \cdot \frac{7}{3}$

STEP 6

Perform the multiplication on the right side of the equation.
$x = \frac{3 \cdot 7}{3}$

STEP 7

Cancel the common factor of 3 in the numerator and the denominator.
$x = \frac{7}{1}$

STEP 8

Simplify the fraction to find the value of $x$ .
$x = 7$
The solution to the equation $\frac{3}{7} x + 5 = 8$ is $x = 7$ .

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Solve the equation 37x+5=8\frac{3}{7} x + 5 = 873​x+5=8 to find the value of xxx.

STEP 1

Assumptions1. We are given the linear equation 37x+5=8\frac{3}{7} x + 5 = 873​x+5=8.2. We need to solve for the variable xxx.

STEP 2

First, we want to isolate the term containing xxx on one side of the equation. We can do this by subtracting 5 from both sides of the equation.37x+5−5=8−5\frac{3}{7} x + 5 - 5 = 8 - 573​x+5−5=8−5

STEP 3

Perform the subtraction on both sides of the equation.37x=3\frac{3}{7} x = 373​x=3

STEP 4

Now, we need to solve for xxx by getting rid of the fraction. We can do this by multiplying both sides of the equation by the reciprocal of 37\frac{3}{7}73​, which is 73\frac{7}{3}37​.73⋅37x=3⋅73\frac{7}{3} \cdot \frac{3}{7} x = 3 \cdot \frac{7}{3}37​⋅73​x=3⋅37​

STEP 5

Simplify both sides of the equation. On the left side, the 73\frac{7}{3}37​ and 37\frac{3}{7}73​ will cancel each other out, leaving us with xxx. On the right side, we multiply 3 by 73\frac{7}{3}37​.x=3⋅73x = 3 \cdot \frac{7}{3}x=3⋅37​

STEP 6

Perform the multiplication on the right side of the equation.x=3⋅73x = \frac{3 \cdot 7}{3}x=33⋅7​

STEP 7

Cancel the common factor of 3 in the numerator and the denominator.x=71x = \frac{7}{1}x=17​

STEP 8

Simplify the fraction to find the value of xxx.x=7x = 7x=7The solution to the equation 37x+5=8\frac{3}{7} x + 5 = 873​x+5=8 is x=7x = 7x=7.

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Solve the equation $\frac{3}{7} x + 5 = 8$ to find the value of $x$ .

Assumptions
1. We are given the linear equation $\frac{3}{7} x + 5 = 8$ .
2. We need to solve for the variable $x$ .

First, we want to isolate the term containing $x$ on one side of the equation. We can do this by subtracting 5 from both sides of the equation.
$\frac{3}{7} x + 5 - 5 = 8 - 5$

Perform the subtraction on both sides of the equation.
$\frac{3}{7} x = 3$

Now, we need to solve for $x$ by getting rid of the fraction. We can do this by multiplying both sides of the equation by the reciprocal of $\frac{3}{7}$ , which is $\frac{7}{3}$ .
$\frac{7}{3} \cdot \frac{3}{7} x = 3 \cdot \frac{7}{3}$

Simplify both sides of the equation. On the left side, the $\frac{7}{3}$ and $\frac{3}{7}$ will cancel each other out, leaving us with $x$ . On the right side, we multiply 3 by $\frac{7}{3}$ .
$x = 3 \cdot \frac{7}{3}$

Perform the multiplication on the right side of the equation.
$x = \frac{3 \cdot 7}{3}$

Cancel the common factor of 3 in the numerator and the denominator.
$x = \frac{7}{1}$

Simplify the fraction to find the value of $x$ .
$x = 7$
The solution to the equation $\frac{3}{7} x + 5 = 8$ is $x = 7$ .