Explanation:
First one:
Calculate the difference:
12 × ( -15/12x ) = 7
Multiplying a positive and a negative equals a negative: (+) × (-) = (-)
-12 × 15/12x = 7
Cancel the greatest common factor 12
-5x = 7
Divide both sides of he equation by -5
Solution: x = -7/5
Second one:
26 × (7y + 5 +3) = 1300
Divide both sides of the equation by 26
7y + 5 + 3 = 50
add the numbers
7y + 8 = 50
Move the constant to the right hand side and change it's sign.
7y = 50 - 8
Subtract the numbers
7y = 48
Divide both sides of the equation by 7
= y = 6
Third One:
Convert the fraction into decimal:
37/10 ÷ (1 2/9 - 0.4)
Convert the mixed number into an improper fraction
37/10 ÷ (11/9 - 0.4)
Convert the decimal into fraction
37/10 ÷ (11/9 - 2/5)
Subtract the fractions
37/10 ÷ 37/45
To divide by a fraction, multiply by the reciprocal of that fraction.
37/ 10 × 45/37
Cancel out the greatest common factor 37
1/10 × 45
Cancel out the greatest common factor 5
1/2 × 9
Calculate the product
Solution: 9/2
Fourth One:
Convert the decimal into fraction and mixed fraction into improper fraction.
1/2 + 1/18
________
(7/6 - 7/18) ÷ 14/5
Add and subtract the fractions
5/9
____
7/9 ÷ 14/5
To divide by a fraction, Multiply by the reciprocal of that fraction.
5/9
____
7/9 × 5/14
Cancel out the greatest common factor 7.
5/9
____
1/9 × 5/2
Multiply the fractions
5/9
____
5/18
Simply the complex fraction
Solution: 2
Fifth one:
Multiply the brackets
0.5x - 6 + 0.2x + 1.4 = 0.3x + 3.4
Collect like terms and simplify
0.7x - 4.6 = 0.3x + 3.4
Move the variable to the left hand side and move the constant to the right hand side and change the signs.
0.7x - 0.3x = 4.6 + 3.4
Simplify
0.4x = 8
Divide both sides of the equation by 0.4
Solution: x = 20
Thank you!