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# A number of algebra practice questions and solutions

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Evaluate.

((-1)2 - 3)3 + 5 · (-5)

Simplify the following expression:

When converting from Fahrenheit degrees to Celsius degrees , a well known formula is used:
. Solve for .

Simplify.

Simplify.

Simplify.

Rewrite the following without an exponent.

Simplify.

Simplify.
3w2w-2 · 4v-9v · 2x-8x8

Simplify.

Multiply.

Multiply.

Rewrite without parentheses and simplify.

Multiply.

Factor
.
Factor.

Factor.

Factor:

Factor:
.

Simplify.
21n4/3x4y2 / 7mn2/9x3y

Simplify.

Solve for :
.

Solve for .

Solve the following proportion for .

Milan runs miles in minutes. At the same rate, how many miles would he run in minutes?

Rewrite the following in simplified radical form.

Assume that all variables represent positive real numbers.

Simplify as much as possible.

Assume that all variables represent positive real numbers.

Simplify.

Assume that all variables represent positive real numbers.
Rationalize the denominator and simplify.

Solve for , where is a real number.

Solve for , where is a real number.

Find the value of .

Write the following in simplified radical form.

Solve for .

Solve the equation

for .

Solve , where is a real number.

Use the quadratic formula to solve for .

Write in simplified radical form by rationalizing the denominator.

Simplify.

Assume that all variables represent positive real numbers.
Multiply.

Simplify as much as possible.

Assume that all variables represent positive real numbers.

Simplify.

Use the quadratic formula to solve for .

Solve for .

Simplify.

Rewrite the following without an exponent.

https://brainmass.com/math/basic-algebra/number-algebra-practice-questions-solutions-354674

#### Solution Preview

Evaluate.

((-1)2 - 3)3 + 5 · (-5)

= {(-1 x -1) - 3}3 + 5 x -5

= {1 - 3}3 - 25

= {-2}3 - 25 = -8 - 25

= - 33

Simplify the following expression:

= -2w -2u -3*(-4u) -3*(-6u)

= -2w - 2u +12u +18u

= 10w + 16u

When converting from Fahrenheit degrees to Celsius degrees , a well known formula is used:
. Solve for .

9C = 5{F - 32}

9C = 5F - 5 x 32

9C = 5F - 160

5F = 9C + 160

F = {9C + 160}/5

F = 9/5*{C +160/9}

Simplify.

= y1 x y5 x y3

= y(1 + 5 + 3)

= y9

Simplify.

= z(6 - 5)*x(3 - 4)

= z*x-1

= z/x

Simplify.

= {x4}3/({-2}3{y}3)

= x(4 x 3)/{(-2 x -2 x -2)*y3}

= x12/-8y3

= -x12/8y3

Rewrite the following without an exponent.

Exponent of -1 means invert the fraction so

= 7/8

Simplify.

= u(-5 x 4)

= u-20

The negative exponent means invert and turn the exponent to a positive thus

= 1/u20

Simplify.
3w2w-2 · 4v-9v · 2x-8x8

= 3w(2 - 2). 4v(1 - 9).2x(8 - 8)

= 3*4*2w0.v-8.x0

Any variable to the power of zero is just 1 thus

= 24v-8

A negative exponent means we invert the variable v and change the expeonent to a positive exponent thus

= 24/v8

Simplify.

= -5u2 + 2u + 1 - 7u + 8 -2u2 -1(4u) -1(-1)
= -5u2 - 2u2 +2u - 7u - 4u + 8 + 1 + 1
Collect u2 , u and number terms together we get
= -7u2 - 9u + 10

Multiply.

= 4*3*4w(4 + 2).v(1 + 9)

= 48w6.v10
Multiply.

= x*x +7*x - 3*x -3(7)

= x2 +4x - 21
Rewrite without parentheses and simplify.

= (3u - 2)*(3u - 2)

= 3u*3u -2(3u) -2(3u) -2(-2)

= 9u2 - 6u - 6u + 4

= 9u2 - 12u + 4

Multiply.