Question

1) 2+x/4=x=5. 2) 7+x/4=x+5 3) 5x+1/7+5=x

Answer 1

2) 7+x/4=x+5 х=8/3

3) 5x+1/7+5=x х=-9/7

Answer 2

Let's solve each equation step by step:

1. $2 + \frac{x}{4} = x + 5$

To solve this equation, we need to isolate the variable $x$ on one side of the equation.

Step 1: Remove the fraction by multiplying both sides by 4 to eliminate the denominator:

$4 \cdot \left(2 + \frac{x}{4}\right) = 4 \cdot (x + 5)$

Simplifying:

$8 + x = 4x + 20$

Step 2: Move all terms with $x$ to one side of the equation, and the constant terms to the other side:

$x - 4x = 20 - 8$

$3x = 12$

Step 3: Divide both sides by 3 to isolate $x$:

$x = \frac{12}{3}$

$x = 4$

So, the solution to the first equation is $x = 4$.

2. $7 + \frac{x}{4} = x + 5$

We'll follow the same steps as above to solve this equation.

Step 1: Remove the fraction by multiplying both sides by 4:

$4 \cdot \left(7 + \frac{x}{4}\right) = 4 \cdot (x + 5)$

Simplifying:

$28 + x = 4x + 20$

Step 2: Move all terms with $x$ to one side and constant terms to the other side:

$x - 4x = 20 - 28$

$-3x = -8$

Step 3: Divide both sides by -3 to solve for $x$:

$x = \frac{-8}{-3}$

$x = \frac{8}{3}$

So, the solution to the second equation is $x = \frac{8}{3}$ or approximately 2.67.

3. $5x + \frac{1}{7} + 5 = x$

We'll solve this equation step by step as well.

Step 1: Combine the constant terms on the left side of the equation:

$5x + 5 + \frac{1}{7} = x$

Step 2: Remove the fraction by multiplying both sides by 7:

$7 \cdot (5x + 5) + 1 = 7x$

$35x + 35 + 1 = 7x$

Step 3: Move all terms with $x$ to one side and constant terms to the other side:

$35x - 7x = -36$

$28x = -36$

Step 4: Divide both sides by 28 to solve for $x$:

$x = \frac{-36}{28}$

Simplify the fraction:

$x = \frac{-9}{7}$

So, the solution to the third equation is $x = \frac{-9}{7}$ or approximately -1.29.

To summarize:

1. $x = 4$

2. $x = \frac{8}{3}$ (or approximately 2.67)

3. $x = \frac{-9}{7}$ (or approximately -1.29)