Question Find the value of $x$ that satisfies the equation $x \cdot \frac{3}{4} = 6$ .

Studdy Solution

STEP 1

Assumptions1. The equation given is $x \cdot \frac{3}{4} x=6$ . We are solving for the variable $x$

STEP 2

First, we need to understand the equation. The equation is a product of $x$ and $\frac{}{4}x$ , which equals6.
$x \cdot \frac{}{4} x=6$

STEP 3

This equation can be rewritten as a quadratic equation. To do this, we multiply $x$ by $\frac{3}{}x$ to get $\frac{3}{}x^2$ .
$\frac{3}{}x^2=6$

STEP 4

To solve for $x$ , we need to isolate $x^2$ on one side of the equation. We can do this by multiplying both sides of the equation by $\frac{4}{3}$ .
$x^2=\frac{4}{3} \cdot6$

STEP 5

Now, calculate the right side of the equation.
$x^2=\frac{4}{3} \cdot =8$

STEP 6

Now that we have $x^2=8$ , we can solve for $x$ by taking the square root of both sides. Remember, when we take the square root of both sides, we get two solutions one positive and one negative.
$x=\sqrt{8} \quad \text{and} \quad x=-\sqrt{8}$

STEP 7

Finally, calculate the square root of to get the two possible values for $x$ .
$x=\sqrt{} =2\sqrt{2} \quad \text{and} \quad x=-\sqrt{} = -2\sqrt{2}$ The solutions for $x$ are $2\sqrt{2}$ and $-2\sqrt{2}$ .

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Question Find the value of $x$ that satisfies the equation $x \cdot \frac{3}{4} = 6$ .

Studdy Solution

STEP 1

Assumptions1. The equation given is $x \cdot \frac{3}{4} x=6$ . We are solving for the variable $x$

STEP 2

First, we need to understand the equation. The equation is a product of $x$ and $\frac{}{4}x$ , which equals6.
$x \cdot \frac{}{4} x=6$

STEP 3

This equation can be rewritten as a quadratic equation. To do this, we multiply $x$ by $\frac{3}{}x$ to get $\frac{3}{}x^2$ .
$\frac{3}{}x^2=6$

STEP 4

To solve for $x$ , we need to isolate $x^2$ on one side of the equation. We can do this by multiplying both sides of the equation by $\frac{4}{3}$ .
$x^2=\frac{4}{3} \cdot6$

STEP 5

Now, calculate the right side of the equation.
$x^2=\frac{4}{3} \cdot =8$

STEP 6

Now that we have $x^2=8$ , we can solve for $x$ by taking the square root of both sides. Remember, when we take the square root of both sides, we get two solutions one positive and one negative.
$x=\sqrt{8} \quad \text{and} \quad x=-\sqrt{8}$

STEP 7

Finally, calculate the square root of to get the two possible values for $x$ .
$x=\sqrt{} =2\sqrt{2} \quad \text{and} \quad x=-\sqrt{} = -2\sqrt{2}$ The solutions for $x$ are $2\sqrt{2}$ and $-2\sqrt{2}$ .

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Question Find the value of xxx that satisfies the equation x⋅34=6x \cdot \frac{3}{4} = 6x⋅43​=6.

Studdy Solution

STEP 1

Assumptions1. The equation given is x⋅34x=6x \cdot \frac{3}{4} x=6x⋅43​x=6 . We are solving for the variable xxx

STEP 2

First, we need to understand the equation. The equation is a product of xxx and 4x\frac{}{4}x4​x, which equals6.x⋅4x=6x \cdot \frac{}{4} x=6x⋅4​x=6

STEP 3

This equation can be rewritten as a quadratic equation. To do this, we multiply xxx by 3x\frac{3}{}x3​x to get 3x2\frac{3}{}x^23​x2.3x2=6\frac{3}{}x^2=63​x2=6

STEP 4

To solve for xxx, we need to isolate x2x^2x2 on one side of the equation. We can do this by multiplying both sides of the equation by 43\frac{4}{3}34​.x2=43⋅6x^2=\frac{4}{3} \cdot6x2=34​⋅6

STEP 5

Now, calculate the right side of the equation.x2=43⋅=8x^2=\frac{4}{3} \cdot =8x2=34​⋅=8

STEP 6

Now that we have x2=8x^2=8x2=8, we can solve for xxx by taking the square root of both sides. Remember, when we take the square root of both sides, we get two solutions one positive and one negative.x=8andx=−8x=\sqrt{8} \quad \text{and} \quad x=-\sqrt{8}x=8​andx=−8​

STEP 7

Finally, calculate the square root of to get the two possible values for xxx.x==22andx=−=−22x=\sqrt{} =2\sqrt{2} \quad \text{and} \quad x=-\sqrt{} = -2\sqrt{2}x=​=22​andx=−​=−22​The solutions for xxx are 222\sqrt{2}22​ and −22-2\sqrt{2}−22​.

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Question Find the value of $x$ that satisfies the equation $x \cdot \frac{3}{4} = 6$ .

Assumptions1. The equation given is $x \cdot \frac{3}{4} x=6$ . We are solving for the variable $x$

First, we need to understand the equation. The equation is a product of $x$ and $\frac{}{4}x$ , which equals6.
$x \cdot \frac{}{4} x=6$

This equation can be rewritten as a quadratic equation. To do this, we multiply $x$ by $\frac{3}{}x$ to get $\frac{3}{}x^2$ .
$\frac{3}{}x^2=6$

To solve for $x$ , we need to isolate $x^2$ on one side of the equation. We can do this by multiplying both sides of the equation by $\frac{4}{3}$ .
$x^2=\frac{4}{3} \cdot6$

Now, calculate the right side of the equation.
$x^2=\frac{4}{3} \cdot =8$

Now that we have $x^2=8$ , we can solve for $x$ by taking the square root of both sides. Remember, when we take the square root of both sides, we get two solutions one positive and one negative.
$x=\sqrt{8} \quad \text{and} \quad x=-\sqrt{8}$

Finally, calculate the square root of to get the two possible values for $x$ .
$x=\sqrt{} =2\sqrt{2} \quad \text{and} \quad x=-\sqrt{} = -2\sqrt{2}$ The solutions for $x$ are $2\sqrt{2}$ and $-2\sqrt{2}$ .