Solved on Jan 18, 2024

Solve the equation $\frac{4}{x+7}=2$ and select the correct solution from the options provided.

STEP 1

Assumptions
1. We are given the equation $\frac{4}{x+7}=2$ .
2. We need to solve for the variable $x$ .
3. The solution must be one of the provided options: a) no solution, b) $x=1$ , c) $x=-7$ , d) $x=-5$ .

STEP 2

To solve for $x$ , we need to isolate the variable on one side of the equation. We can start by multiplying both sides of the equation by the denominator $(x+7)$ to eliminate the fraction.
$(x+7) \cdot \frac{4}{x+7} = 2 \cdot (x+7)$

STEP 3

On the left side of the equation, the $(x+7)$ in the numerator and denominator cancel out, leaving us with:
$4 = 2 \cdot (x+7)$

STEP 4

Now, distribute the 2 on the right side of the equation:
$4 = 2x + 14$

STEP 5

Next, we want to isolate $x$ by moving the constant term on the right side to the left side. We can do this by subtracting 14 from both sides of the equation:
$4 - 14 = 2x + 14 - 14$

STEP 6

Simplify both sides of the equation:
$-10 = 2x$

STEP 7

Now, divide both sides of the equation by 2 to solve for $x$ :
$\frac{-10}{2} = \frac{2x}{2}$

STEP 8

Simplify the equation to find the value of $x$ :
$x = -5$
The solution to the equation $\frac{4}{x+7}=2$ is $x=-5$ , which corresponds to option d).

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Solve the equation $\frac{4}{x+7}=2$ and select the correct solution from the options provided.

STEP 1

Assumptions
1. We are given the equation $\frac{4}{x+7}=2$ .
2. We need to solve for the variable $x$ .
3. The solution must be one of the provided options: a) no solution, b) $x=1$ , c) $x=-7$ , d) $x=-5$ .

STEP 2

To solve for $x$ , we need to isolate the variable on one side of the equation. We can start by multiplying both sides of the equation by the denominator $(x+7)$ to eliminate the fraction.
$(x+7) \cdot \frac{4}{x+7} = 2 \cdot (x+7)$

STEP 3

On the left side of the equation, the $(x+7)$ in the numerator and denominator cancel out, leaving us with:
$4 = 2 \cdot (x+7)$

STEP 4

Now, distribute the 2 on the right side of the equation:
$4 = 2x + 14$

STEP 5

Next, we want to isolate $x$ by moving the constant term on the right side to the left side. We can do this by subtracting 14 from both sides of the equation:
$4 - 14 = 2x + 14 - 14$

STEP 6

Simplify both sides of the equation:
$-10 = 2x$

STEP 7

Now, divide both sides of the equation by 2 to solve for $x$ :
$\frac{-10}{2} = \frac{2x}{2}$

STEP 8

Simplify the equation to find the value of $x$ :
$x = -5$
The solution to the equation $\frac{4}{x+7}=2$ is $x=-5$ , which corresponds to option d).

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Solve the equation 4x+7=2\frac{4}{x+7}=2x+74​=2 and select the correct solution from the options provided.

STEP 1

Assumptions1. We are given the equation 4x+7=2\frac{4}{x+7}=2x+74​=2.2. We need to solve for the variable xxx.3. The solution must be one of the provided options: a) no solution, b) x=1x=1x=1, c) x=−7x=-7x=−7, d) x=−5x=-5x=−5.

STEP 2

To solve for xxx, we need to isolate the variable on one side of the equation. We can start by multiplying both sides of the equation by the denominator (x+7)(x+7)(x+7) to eliminate the fraction.(x+7)⋅4x+7=2⋅(x+7) (x+7) \cdot \frac{4}{x+7} = 2 \cdot (x+7) (x+7)⋅x+74​=2⋅(x+7)

STEP 3

On the left side of the equation, the (x+7)(x+7)(x+7) in the numerator and denominator cancel out, leaving us with:4=2⋅(x+7) 4 = 2 \cdot (x+7) 4=2⋅(x+7)

STEP 4

Now, distribute the 2 on the right side of the equation:4=2x+14 4 = 2x + 14 4=2x+14

STEP 5

Next, we want to isolate xxx by moving the constant term on the right side to the left side. We can do this by subtracting 14 from both sides of the equation:4−14=2x+14−14 4 - 14 = 2x + 14 - 14 4−14=2x+14−14

STEP 6

Simplify both sides of the equation:−10=2x -10 = 2x −10=2x

STEP 7

Now, divide both sides of the equation by 2 to solve for xxx:−102=2x2 \frac{-10}{2} = \frac{2x}{2} 2−10​=22x​

STEP 8

Simplify the equation to find the value of xxx:x=−5 x = -5 x=−5The solution to the equation 4x+7=2\frac{4}{x+7}=2x+74​=2 is x=−5x=-5x=−5, which corresponds to option d).

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Solve the equation $\frac{4}{x+7}=2$ and select the correct solution from the options provided.

Assumptions
1. We are given the equation $\frac{4}{x+7}=2$ .
2. We need to solve for the variable $x$ .
3. The solution must be one of the provided options: a) no solution, b) $x=1$ , c) $x=-7$ , d) $x=-5$ .

To solve for $x$ , we need to isolate the variable on one side of the equation. We can start by multiplying both sides of the equation by the denominator $(x+7)$ to eliminate the fraction.
$(x+7) \cdot \frac{4}{x+7} = 2 \cdot (x+7)$

On the left side of the equation, the $(x+7)$ in the numerator and denominator cancel out, leaving us with:
$4 = 2 \cdot (x+7)$

Now, distribute the 2 on the right side of the equation:
$4 = 2x + 14$

Next, we want to isolate $x$ by moving the constant term on the right side to the left side. We can do this by subtracting 14 from both sides of the equation:
$4 - 14 = 2x + 14 - 14$

Simplify both sides of the equation:
$-10 = 2x$

Now, divide both sides of the equation by 2 to solve for $x$ :
$\frac{-10}{2} = \frac{2x}{2}$

Simplify the equation to find the value of $x$ :
$x = -5$
The solution to the equation $\frac{4}{x+7}=2$ is $x=-5$ , which corresponds to option d).