Question Solve the equation $\frac{10.4-x}{1.2}=1.6$ for the unknown variable $x$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $\frac{10.4-x}{1.2}=1.6$ .
2. We need to solve for $x$ .

STEP 2

To isolate the variable $x$ , we first need to eliminate the denominator. We can do this by multiplying both sides of the equation by the denominator, which is $1.2$ .
$1.2 \times \frac{10.4-x}{1.2} = 1.2 \times 1.6$

STEP 3

On the left side, the $1.2$ in the numerator and denominator cancel out, leaving us with:
$10.4 - x = 1.2 \times 1.6$

STEP 4

Now, we calculate the right side of the equation by multiplying $1.2$ by $1.6$ .
$10.4 - x = 1.92$

STEP 5

Next, we want to isolate $x$ on one side of the equation. To do this, we will move the term without $x$ (which is $10.4$ ) to the other side by subtracting $10.4$ from both sides of the equation.
$10.4 - x - 10.4 = 1.92 - 10.4$

STEP 6

Perform the subtraction on both sides to find the value of $-x$ .
$-x = 1.92 - 10.4$

STEP 7

Calculate the result of the subtraction.
$-x = -8.48$

STEP 8

To find the value of $x$ , we need to multiply both sides of the equation by $-1$ to get rid of the negative sign.
$-1 \times (-x) = -1 \times (-8.48)$

STEP 9

Multiply by $-1$ to find the value of $x$ .
$x = 8.48$
The solution to the equation $\frac{10.4-x}{1.2}=1.6$ is $x = 8.48$ .

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Question Solve the equation $\frac{10.4-x}{1.2}=1.6$ for the unknown variable $x$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $\frac{10.4-x}{1.2}=1.6$ .
2. We need to solve for $x$ .

STEP 2

To isolate the variable $x$ , we first need to eliminate the denominator. We can do this by multiplying both sides of the equation by the denominator, which is $1.2$ .
$1.2 \times \frac{10.4-x}{1.2} = 1.2 \times 1.6$

STEP 3

On the left side, the $1.2$ in the numerator and denominator cancel out, leaving us with:
$10.4 - x = 1.2 \times 1.6$

STEP 4

Now, we calculate the right side of the equation by multiplying $1.2$ by $1.6$ .
$10.4 - x = 1.92$

STEP 5

Next, we want to isolate $x$ on one side of the equation. To do this, we will move the term without $x$ (which is $10.4$ ) to the other side by subtracting $10.4$ from both sides of the equation.
$10.4 - x - 10.4 = 1.92 - 10.4$

STEP 6

Perform the subtraction on both sides to find the value of $-x$ .
$-x = 1.92 - 10.4$

STEP 7

Calculate the result of the subtraction.
$-x = -8.48$

STEP 8

To find the value of $x$ , we need to multiply both sides of the equation by $-1$ to get rid of the negative sign.
$-1 \times (-x) = -1 \times (-8.48)$

STEP 9

Multiply by $-1$ to find the value of $x$ .
$x = 8.48$
The solution to the equation $\frac{10.4-x}{1.2}=1.6$ is $x = 8.48$ .

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Question Solve the equation 10.4−x1.2=1.6\frac{10.4-x}{1.2}=1.61.210.4−x​=1.6 for the unknown variable xxx.

Studdy Solution

STEP 1

Assumptions1. We are given the equation 10.4−x1.2=1.6\frac{10.4-x}{1.2}=1.61.210.4−x​=1.6.2. We need to solve for xxx.

STEP 2

To isolate the variable xxx, we first need to eliminate the denominator. We can do this by multiplying both sides of the equation by the denominator, which is 1.21.21.2.1.2×10.4−x1.2=1.2×1.61.2 \times \frac{10.4-x}{1.2} = 1.2 \times 1.61.2×1.210.4−x​=1.2×1.6

STEP 3

On the left side, the 1.21.21.2 in the numerator and denominator cancel out, leaving us with:10.4−x=1.2×1.610.4 - x = 1.2 \times 1.610.4−x=1.2×1.6

STEP 4

Now, we calculate the right side of the equation by multiplying 1.21.21.2 by 1.61.61.6.10.4−x=1.9210.4 - x = 1.9210.4−x=1.92

STEP 5

Next, we want to isolate xxx on one side of the equation. To do this, we will move the term without xxx (which is 10.410.410.4) to the other side by subtracting 10.410.410.4 from both sides of the equation.10.4−x−10.4=1.92−10.410.4 - x - 10.4 = 1.92 - 10.410.4−x−10.4=1.92−10.4

STEP 6

Perform the subtraction on both sides to find the value of −x-x−x.−x=1.92−10.4-x = 1.92 - 10.4−x=1.92−10.4

STEP 7

Calculate the result of the subtraction.−x=−8.48-x = -8.48−x=−8.48

STEP 8

To find the value of xxx, we need to multiply both sides of the equation by −1-1−1 to get rid of the negative sign.−1×(−x)=−1×(−8.48)-1 \times (-x) = -1 \times (-8.48)−1×(−x)=−1×(−8.48)

STEP 9

Multiply by −1-1−1 to find the value of xxx.x=8.48x = 8.48x=8.48The solution to the equation 10.4−x1.2=1.6\frac{10.4-x}{1.2}=1.61.210.4−x​=1.6 is x=8.48x = 8.48x=8.48.

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Question Solve the equation $\frac{10.4-x}{1.2}=1.6$ for the unknown variable $x$ .

Assumptions
1. We are given the equation $\frac{10.4-x}{1.2}=1.6$ .
2. We need to solve for $x$ .

To isolate the variable $x$ , we first need to eliminate the denominator. We can do this by multiplying both sides of the equation by the denominator, which is $1.2$ .
$1.2 \times \frac{10.4-x}{1.2} = 1.2 \times 1.6$

On the left side, the $1.2$ in the numerator and denominator cancel out, leaving us with:
$10.4 - x = 1.2 \times 1.6$

Now, we calculate the right side of the equation by multiplying $1.2$ by $1.6$ .
$10.4 - x = 1.92$

Next, we want to isolate $x$ on one side of the equation. To do this, we will move the term without $x$ (which is $10.4$ ) to the other side by subtracting $10.4$ from both sides of the equation.
$10.4 - x - 10.4 = 1.92 - 10.4$

Perform the subtraction on both sides to find the value of $-x$ .
$-x = 1.92 - 10.4$

Calculate the result of the subtraction.
$-x = -8.48$

To find the value of $x$ , we need to multiply both sides of the equation by $-1$ to get rid of the negative sign.
$-1 \times (-x) = -1 \times (-8.48)$

Multiply by $-1$ to find the value of $x$ .
$x = 8.48$
The solution to the equation $\frac{10.4-x}{1.2}=1.6$ is $x = 8.48$ .