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Solving equations...!!!

1. Simplify: 4[a - b(2 + 3a)] - 3a[2+b(4 - a)]
2. Simplify: (7x2 - 2y + z) + (3y - z) + (4x2 - 6y)
3. Simplify: (8x2 - xy + 4y2) - (12x2 - y2 + 7xy)
4. Simplify: (12x2y2 - 15xy2)/(3xy)
5. Simplify: 5x[(3x2 + x - 4) + (9x2 - 6x)/(3x)]
6. Simplify: 8 - {3x + 9y - (2x - y) + 8x + 5y}

7.If P = 2y - 6xy - 3x and Q = 4 - 5y, find 2P - 3Q and simplify the answer.

8. A woman buys three board games for $107.10, including tax. If each board game cost $34, what was the sales tax rate?

9. Sandy has $3.25 in change. She has five more dimes than quarters but twice as many nickels as dimes. Express the given information as an algebraic equation and simplify. [I am not required to solve the problem.]

10. Jim's nephew owns a triangular plot of land. The perimeter fence that surrounds the land measures 121 feet. The shortest side is 15 feet longer than one-half of the longest side. The second longest side is 4 feet shorter than the longest side. What is the length of each side?

Solution Preview

Please find the solution properly described in the attached file.

1. Simplify: 4[a - b(2 + 3a)] - 3a[2+b(4 - a)]

Answer -

4[a - b(2 + 3a)] - 3a[2+b(4 - a)]

or, 4[a - 2b - 3ab] - 3a[2 + 4b - ab]

or, (4a - 8b - 12ab) - (6a + 12ab - 3a2b)

or, 4a - 8b - 12ab -6a - 12ab + 3a2b

or, -2a - 8b - 24ab - 3a2b.

2. Simplify: (7x2 - 2y + z) + (3y - z) + (4x2 - 6y)

Answer -

(7x2 - 2y + z) + (3y - z) + (4x2 - 6y)

or, 7x2 - 2y + z + 3y - z + 4x2 - 6y

or, 7x2 + 4x2 - 2y + 3y- 6y + z - z

or, 11x2 - 5y

or, 11x2 - 5y.

3. Simplify: (8x2 - xy + 4y2) - (12x2 - y2 + 7xy)

Answer -

(8x2 - xy + 4y2) - (12x2 - y2 + 7xy)

or, 8x2 - xy + 4y2 -12x2 + y2 - 7xy

or, 8x2 - 12x2 + 4y2 + y2- xy - 7xy

or, -4x2 + 5y2 - 8xy

or, -4x2 + 5y2 - 8xy.

4. Simplify: (12x2y2 - 15xy2)/(3xy)

Answer -

Taking 3xy common in the numerator, we have -

Cancelling out the 3xy from the numerator and the denominator we have -

4xy - 5y as the ...

Solution Summary

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