Solved on Jan 24, 2024

Solve the linear equation $3.25(x-2)=19.5$ for the unknown variable $x$ .

STEP 1

Assumptions
1. We are given the equation $3.25(x-2) = 19 \frac{1}{2}$ .
2. We need to solve for $x$ .

STEP 2

First, we need to simplify the right side of the equation by converting the mixed number to an improper fraction.
$19 \frac{1}{2} = 19 \times \frac{2}{2} + \frac{1}{2}$

STEP 3

Now, perform the multiplication and addition to find the improper fraction.
$19 \times \frac{2}{2} + \frac{1}{2} = \frac{38}{2} + \frac{1}{2}$

STEP 4

Add the fractions to get a single improper fraction.
$\frac{38}{2} + \frac{1}{2} = \frac{39}{2}$

STEP 5

Now that we have simplified the right side of the equation, we can rewrite the equation as:
$3.25(x-2) = \frac{39}{2}$

STEP 6

To solve for $x$ , we first need to isolate the term containing $x$ . We can do this by dividing both sides of the equation by $3.25$ .
$\frac{3.25(x-2)}{3.25} = \frac{\frac{39}{2}}{3.25}$

STEP 7

Perform the division on the left side of the equation to remove the coefficient of $x$ .
$x - 2 = \frac{\frac{39}{2}}{3.25}$

STEP 8

To perform the division on the right side, we can convert $3.25$ to a fraction.
$3.25 = \frac{325}{100} = \frac{13}{4}$

STEP 9

Now, rewrite the equation using the fraction for $3.25$ .
$x - 2 = \frac{\frac{39}{2}}{\frac{13}{4}}$

STEP 10

To divide by a fraction, we multiply by its reciprocal.
$x - 2 = \frac{39}{2} \times \frac{4}{13}$

STEP 11

Now, perform the multiplication on the right side.
$x - 2 = \frac{39 \times 4}{2 \times 13}$

STEP 12

Simplify the multiplication by canceling out common factors.
$x - 2 = \frac{39}{13} \times 2$

STEP 13

Simplify the fraction.
$x - 2 = 3 \times 2$

STEP 14

Now, perform the multiplication.
$x - 2 = 6$

STEP 15

To solve for $x$ , add $2$ to both sides of the equation.
$x = 6 + 2$

STEP 16

Finally, calculate the value of $x$ .
$x = 8$
The solution to the equation $3.25(x-2) = 19 \frac{1}{2}$ is $x = 8$ .

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Solve the linear equation $3.25(x-2)=19.5$ for the unknown variable $x$ .

STEP 1

Assumptions
1. We are given the equation $3.25(x-2) = 19 \frac{1}{2}$ .
2. We need to solve for $x$ .

STEP 2

First, we need to simplify the right side of the equation by converting the mixed number to an improper fraction.
$19 \frac{1}{2} = 19 \times \frac{2}{2} + \frac{1}{2}$

STEP 3

Now, perform the multiplication and addition to find the improper fraction.
$19 \times \frac{2}{2} + \frac{1}{2} = \frac{38}{2} + \frac{1}{2}$

STEP 4

Add the fractions to get a single improper fraction.
$\frac{38}{2} + \frac{1}{2} = \frac{39}{2}$

STEP 5

Now that we have simplified the right side of the equation, we can rewrite the equation as:
$3.25(x-2) = \frac{39}{2}$

STEP 6

To solve for $x$ , we first need to isolate the term containing $x$ . We can do this by dividing both sides of the equation by $3.25$ .
$\frac{3.25(x-2)}{3.25} = \frac{\frac{39}{2}}{3.25}$

STEP 7

Perform the division on the left side of the equation to remove the coefficient of $x$ .
$x - 2 = \frac{\frac{39}{2}}{3.25}$

STEP 8

To perform the division on the right side, we can convert $3.25$ to a fraction.
$3.25 = \frac{325}{100} = \frac{13}{4}$

STEP 9

Now, rewrite the equation using the fraction for $3.25$ .
$x - 2 = \frac{\frac{39}{2}}{\frac{13}{4}}$

STEP 10

To divide by a fraction, we multiply by its reciprocal.
$x - 2 = \frac{39}{2} \times \frac{4}{13}$

STEP 11

Now, perform the multiplication on the right side.
$x - 2 = \frac{39 \times 4}{2 \times 13}$

STEP 12

Simplify the multiplication by canceling out common factors.
$x - 2 = \frac{39}{13} \times 2$

STEP 13

Simplify the fraction.
$x - 2 = 3 \times 2$

STEP 14

Now, perform the multiplication.
$x - 2 = 6$

STEP 15

To solve for $x$ , add $2$ to both sides of the equation.
$x = 6 + 2$

STEP 16

Finally, calculate the value of $x$ .
$x = 8$
The solution to the equation $3.25(x-2) = 19 \frac{1}{2}$ is $x = 8$ .

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Solve the linear equation 3.25(x−2)=19.53.25(x-2)=19.53.25(x−2)=19.5 for the unknown variable xxx.

STEP 1

Assumptions1. We are given the equation 3.25(x−2)=19123.25(x-2) = 19 \frac{1}{2}3.25(x−2)=1921​.2. We need to solve for xxx.

STEP 2

First, we need to simplify the right side of the equation by converting the mixed number to an improper fraction.1912=19×22+1219 \frac{1}{2} = 19 \times \frac{2}{2} + \frac{1}{2}1921​=19×22​+21​

STEP 3

Now, perform the multiplication and addition to find the improper fraction.19×22+12=382+1219 \times \frac{2}{2} + \frac{1}{2} = \frac{38}{2} + \frac{1}{2}19×22​+21​=238​+21​

STEP 4

Add the fractions to get a single improper fraction.382+12=392\frac{38}{2} + \frac{1}{2} = \frac{39}{2}238​+21​=239​

STEP 5

Now that we have simplified the right side of the equation, we can rewrite the equation as:3.25(x−2)=3923.25(x-2) = \frac{39}{2}3.25(x−2)=239​

STEP 6

To solve for xxx, we first need to isolate the term containing xxx. We can do this by dividing both sides of the equation by 3.253.253.25.3.25(x−2)3.25=3923.25\frac{3.25(x-2)}{3.25} = \frac{\frac{39}{2}}{3.25}3.253.25(x−2)​=3.25239​​

STEP 7

Perform the division on the left side of the equation to remove the coefficient of xxx.x−2=3923.25x - 2 = \frac{\frac{39}{2}}{3.25}x−2=3.25239​​

STEP 8

To perform the division on the right side, we can convert 3.253.253.25 to a fraction.3.25=325100=1343.25 = \frac{325}{100} = \frac{13}{4}3.25=100325​=413​

STEP 9

Now, rewrite the equation using the fraction for 3.253.253.25.x−2=392134x - 2 = \frac{\frac{39}{2}}{\frac{13}{4}}x−2=413​239​​

STEP 10

To divide by a fraction, we multiply by its reciprocal.x−2=392×413x - 2 = \frac{39}{2} \times \frac{4}{13}x−2=239​×134​

STEP 11

Now, perform the multiplication on the right side.x−2=39×42×13x - 2 = \frac{39 \times 4}{2 \times 13}x−2=2×1339×4​

STEP 12

Simplify the multiplication by canceling out common factors.x−2=3913×2x - 2 = \frac{39}{13} \times 2x−2=1339​×2

STEP 13

Simplify the fraction.x−2=3×2x - 2 = 3 \times 2x−2=3×2

STEP 14

Now, perform the multiplication.x−2=6x - 2 = 6x−2=6

STEP 15

To solve for xxx, add 222 to both sides of the equation.x=6+2x = 6 + 2x=6+2

STEP 16

Finally, calculate the value of xxx.x=8x = 8x=8The solution to the equation 3.25(x−2)=19123.25(x-2) = 19 \frac{1}{2}3.25(x−2)=1921​ is x=8x = 8x=8.

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Solve the linear equation $3.25(x-2)=19.5$ for the unknown variable $x$ .

Assumptions
1. We are given the equation $3.25(x-2) = 19 \frac{1}{2}$ .
2. We need to solve for $x$ .

First, we need to simplify the right side of the equation by converting the mixed number to an improper fraction.
$19 \frac{1}{2} = 19 \times \frac{2}{2} + \frac{1}{2}$

Now, perform the multiplication and addition to find the improper fraction.
$19 \times \frac{2}{2} + \frac{1}{2} = \frac{38}{2} + \frac{1}{2}$

Add the fractions to get a single improper fraction.
$\frac{38}{2} + \frac{1}{2} = \frac{39}{2}$

Now that we have simplified the right side of the equation, we can rewrite the equation as:
$3.25(x-2) = \frac{39}{2}$

To solve for $x$ , we first need to isolate the term containing $x$ . We can do this by dividing both sides of the equation by $3.25$ .
$\frac{3.25(x-2)}{3.25} = \frac{\frac{39}{2}}{3.25}$

Perform the division on the left side of the equation to remove the coefficient of $x$ .
$x - 2 = \frac{\frac{39}{2}}{3.25}$

To perform the division on the right side, we can convert $3.25$ to a fraction.
$3.25 = \frac{325}{100} = \frac{13}{4}$

Now, rewrite the equation using the fraction for $3.25$ .
$x - 2 = \frac{\frac{39}{2}}{\frac{13}{4}}$

To divide by a fraction, we multiply by its reciprocal.
$x - 2 = \frac{39}{2} \times \frac{4}{13}$

Now, perform the multiplication on the right side.
$x - 2 = \frac{39 \times 4}{2 \times 13}$

Simplify the multiplication by canceling out common factors.
$x - 2 = \frac{39}{13} \times 2$

Simplify the fraction.
$x - 2 = 3 \times 2$

Now, perform the multiplication.
$x - 2 = 6$

To solve for $x$ , add $2$ to both sides of the equation.
$x = 6 + 2$

Finally, calculate the value of $x$ .
$x = 8$
The solution to the equation $3.25(x-2) = 19 \frac{1}{2}$ is $x = 8$ .