Question

Yravneniya! 1) 0,8(x-2)+2,6=0,5(7+x) 2) -0,5(x-4)-7,3=0,8(2-x) 3) (1,2-2)(8x+5,6)=0 4) (8y+6)(1,8-0,4y)=0

Answer 1

$1) \: 0.8(x - 2) + 2.6 = 0.5(7 + x) \\ 0.8x - 1.6 + 2.6 = 3.5 + 0.5x \\ 0.8x + 1 = 3.5 + 0.5x \\ 0.8 x - 0.5x = 3.5 - 1 \\ 0.3x = 2.5 \\ x = \frac{25}{3} = 8 \frac{1}{3} \\ 2) \: - 0.5(x - 4) - 7.3 = 0.8(2 - x) \\ - 0.5x + 2 - 7.3 = 1.6 - 0.8x \\ - 0.5x - 5.3 = 1.6 - 0.8x \\ - 0.5x + 0.8x = 1.6 + 5.3 \\ 0.3x = 6.9 \\ x = 23 \\ 3) \: (1.2 - 2) \times (8x + 5.6) = 0 \\ 8x + 5.6 = 0 \\ 8x = - 5.6 \\ x = - 0.7 \\ 4) \: (8y + 6)(1.8 - 0.4y) = 0 \\ (8y + 6)( \frac{9}{5} - \frac{2}{5} y) = 0 \\ \\ 8y + 6 = 0 \\ \frac{9}{5} - \frac{2}{5} y = 0 \\ \\ y1= - \frac{3}{4} \\ y2 = \frac{9}{2}$

Answer 2

Let's solve each of the equations step-by-step:

1. 0.8(x-2) + 2.6 = 0.5(7+x)

Step 1: Distribute the numbers on the right side of the equation. 0.8x - 1.6 + 2.6 = 3.5 + 0.5x

Step 2: Combine like terms. 0.8x + 1 = 3.5 + 0.5x

Step 3: Move the variable terms to one side and the constant terms to the other side. 0.8x - 0.5x = 3.5 - 1

Step 4: Simplify and solve for x. 0.3x = 2.5 x = 2.5 / 0.3 x ≈ 8.3333

So, the solution to the equation is approximately x ≈ 8.3333.

2. -0.5(x-4) - 7.3 = 0.8(2-x)

Step 1: Distribute the numbers on both sides of the equation. -0.5x + 2 - 7.3 = 1.6 - 0.8x

Step 2: Combine like terms. -0.5x - 5.3 = 1.6 - 0.8x

Step 3: Move the variable terms to one side and the constant terms to the other side. -0.5x + 0.8x = 1.6 + 5.3

Step 4: Simplify and solve for x. 0.3x = 6.9 x = 6.9 / 0.3 x ≈ 23

So, the solution to the equation is approximately x ≈ 23.

3. (1.2-2)(8x+5.6) = 0

Step 1: Simplify the expression inside the parentheses. -0.8(8x + 5.6) = 0

Step 2: Distribute the constant. -6.4x - 4.48 = 0

Step 3: Move the variable term to one side and the constant term to the other side. -6.4x = 4.48

Step 4: Solve for x. x = 4.48 / -6.4 x ≈ -0.7

So, the solution to the equation is approximately x ≈ -0.7.

4. (8y+6)(1.8-0.4y) = 0

Step 1: Apply the distributive property. 1.8(8y) + 1.8(-0.4y) - 0.4y(8y) - 0.4y(-0.4y) = 0

Step 2: Simplify each term. 16y + 1.8 - 3.2y^2 + 0.16y^2 = 0

Step 3: Combine like terms. -3.04y^2 + 16y + 1.8 = 0

Step 4: Solve for y using either factoring or the quadratic formula. In this case, we can factor: -0.04(76y^2 - 400y - 45) = 0

Step 5: Solve the quadratic equation 76y^2 - 400y - 45 = 0 You can use the quadratic formula or factor further. After solving, you'll find two solutions for y.

y ≈ 5.2632 or y ≈ 0.2157

So, the solutions to the equation are approximately y ≈ 5.2632 and y ≈ 0.2157.