Question

(20-36/(х/200+4)) -2-22=10

Answer 1

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Answer 2

To solve the equation, we'll follow these steps:

Step 1: Simplify the expression on the left side of the equation. Step 2: Solve for 'x'.

Let's get started:

Step 1: Simplify the expression on the left side of the equation. The equation is:

(20 - 36 / (x / 200 + 4)) - 2 - 22 = 10

First, let's simplify the expression inside the parentheses:

x / 200 + 4

Now, let's find the common denominator for the subtraction:

Common denominator = 200

Rewrite 20 as 200 / 10 and 4 as 200 / 50:

(200 / 10 - 36 / (x / 200 + 4)) - 2 - 22 = 10

Step 2: Combine the fractions:

(200 - 36 / (x / 200 + 4)) - 2 - 22 = 10

Next, let's get rid of the parentheses around the fraction:

(200 - 36) / (x / 200 + 4) - 2 - 22 = 10

Simplify the numerator:

164 / (x / 200 + 4) - 2 - 22 = 10

Step 3: Combine the fractions with a common denominator:

The common denominator is (x / 200 + 4):

[164 - 2(x / 200 + 4) - 22(x / 200 + 4)] / (x / 200 + 4) = 10

Now, let's simplify the numerator further:

[164 - 2x / 100 - 8 - 22x / 100 - 88] / (x / 200 + 4) = 10

Combine like terms:

[164 - (2x + 22x) / 100 - 96] / (x / 200 + 4) = 10

Combine the numerators:

[164 - 24x / 100 - 96] / (x / 200 + 4) = 10

Now, let's work on the numerator:

[164 - 0.24x - 96] / (x / 200 + 4) = 10

Combine like terms:

(68 - 0.24x) / (x / 200 + 4) = 10

Step 4: Remove the fraction by multiplying both sides by (x / 200 + 4):

[(x / 200 + 4) * (68 - 0.24x)] / (x / 200 + 4) = 10 * (x / 200 + 4)

The (x / 200 + 4) term cancels out on the left side:

68 - 0.24x = 10x + 40

Step 5: Now, solve for 'x':

Add 0.24x to both sides:

68 = 10.24x + 40

Subtract 40 from both sides:

28 = 10.24x

Divide by 10.24:

x = 28 / 10.24 ≈ 2.73

So, the solution for 'x' is approximately 2.73.