Question

1) (-4,4÷(-2,1/5)-3,2)×5/6 2) 2(х+1,1/6)-2,1/3=1,5 3) (3,4-1,7х)(2х+8)=0 4)(-2,5+2,1/3)×(-5,1/7)+1,1/3×(-5,6) 5) (1,9-9,5х)(3х+27)=0 6)(1,25-1,1/3)×(-5,1/7)-1,1/6÷5,4/9

Answer 1

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Answer 2

To solve these mathematical expressions, let's perform the calculations step by step:

1. (-4, 4 ÷ (-2, 1/5) - 3, 2) × 5/6

Step 1: Evaluate the expression inside the parentheses first. (-4) ÷ (-2 + 1/5) - 3.2 = -4 ÷ (-2.2) - 3.2

Step 2: Perform the division and subtraction inside the parentheses. -4 ÷ (-2.2) = 1.81818... (repeating decimals) 1.81818... - 3.2 ≈ -1.38182... (repeating decimals)

Step 3: Finally, multiply the result by 5/6. -1.38182... × 5/6 ≈ -1.15152... (repeating decimals)

Answer: Approximately -1.15152... (repeating decimals)

2. 2(x + 1, 1/6) - 2, 1/3 = 1, 5

Step 1: Distribute the 2 across the parentheses. 2x + 2 × 1, 1/6 - 2, 1/3 = 1, 5

Step 2: Convert the mixed numbers to improper fractions. 2x + 13/6 - 7/3 = 1, 5 (since 1 = 6/6)

Step 3: Find a common denominator for the fractions (which is 6). 2x + 13/6 - 14/6 = 1, 5

Step 4: Combine the fractions. 2x - 1/6 = 1, 5

Step 5: Move the constant term to the other side. 2x = 1, 5 + 1/6

Step 6: Convert 1, 5 to an improper fraction. 2x = 9/6 + 1/6

Step 7: Combine the fractions on the right side. 2x = 10/6

Step 8: Divide by 2 to solve for x. x = (10/6) ÷ 2 x = 10/12 x = 5/6

Answer: x = 5/6

3. (3, 4 - 1, 7x)(2x + 8) = 0

To solve this quadratic equation, set each factor to zero and solve for x:

3, 4 - 1, 7x = 0 -1, 7x = -3, 4 x = (-3, 4) ÷ (-1, 7) x ≈ 2

2x + 8 = 0 2x = -8 x = -8 ÷ 2 x = -4

So the solutions for the equation are x = 2 and x = -4.

4. (-2, 5 + 2, 1/3) × (-5, 1/7) + 1, 1/3 × (-5, 6)

Step 1: Convert the mixed numbers to improper fractions. (-2, 5) = -2 - 5/1 = -12/5 (-5, 6) = -5 - 6/1 = -11/6

Step 2: Perform the addition and subtraction inside the parentheses. (-12/5 + 2/3) × (-11/7) + (4/3) × (-28/5)

Step 3: Find a common denominator for the fractions. (-36/15 + 10/15) × (-11/7) + (20/15) × (-84/15)

Step 4: Combine the fractions. (-26/15) × (-11/7) + (-84/15)

Step 5: Multiply the fractions. (286/105) - (84/15)

Step 6: Convert the result to a mixed number. (286/105) - (84/15) = (2, 56/105) - (5, 24/105) = -2, 68/105

Answer: -2, 68/105

5. (1, 9 - 9, 5x)(3x + 27) = 0

To solve this quadratic equation, set each factor to zero and solve for x:

1, 9 - 9, 5x = 0 -9, 5x = -1, 9 x = (-1, 9) ÷ (-9, 5) x ≈ 0, 2

3x + 27 = 0 3x = -27 x = -27 ÷ 3 x = -9

So the solutions for the equation are x = 0, 2 and x = -9.

6. (1, 25 - 1, 1/3) × (-5, 1/7) - 1, 1/6 ÷ 5, 4/9

Step 1: Convert the mixed numbers to improper fractions. (1, 25) = 1 + 25/100 = 125/100 (-5, 1/7) = -5 - 1/7 = -36/7

Step 2: Perform the multiplication and subtraction. (125/100) × (-36/7) - (7/6) ÷ (54/90)

Step 3: Find a common denominator for the fractions. (625/500) × (-180/35) - (105/90) ÷ (54/90)

Step 4: Simplify the fractions. (625/500) × (-36/7) - (7/6) ÷ (54/90)

Step 5: Multiply the fractions. (-22500/35000) - (70/54)

Step 6: Convert the result to a mixed number. (-22500/35000) - (70/54) = (-22500/35000) - (35000/50000) = - (22500/35000) + (35000/50000)

Step 7: Find a common denominator for the fractions. (-22500/35000) + (35000/50000) = (-22500/35000) + (70000/100000)

Step 8: Combine the fractions. (-22500/35000) + (70000/100000) = (-15/23) + (7/10)

Step 9: Find a common denominator for the fractions. (-15/23) + (7/10) = (-150/230) + (161/230)

Step 10: Combine the fractions. (-150/230) + (161/230) = 11/230

Answer: 11/230