Chapter 7

Simplify. $$ 3 x+7 x $$

A positive integer is twice another. The sum of the reciprocals of the two positive integers is \(3 / 10\). Find the two integers.

Simplify. (Assume all denominators are nonzero.) $$ 1254 $$

Translate the following sentences into a mathematical formula. The distance, \(D\), an automobile can travel is directly proportional to the time, \(t\), that it travels at a constant speed.

Evaluate for the given set of \(x\) -values. $$ 5 x ;\\{-1,0,1\\} $$

Evaluate for the given set of \(x\) -values. $$ 252 \times 2 ;\\{-5,0,5\\} $$

Multiply. (Assume all denominators are nonzero.) $$ 2 \times 3 \cdot 94 \times 2 $$

Simplify. $$ 9 x-10 x $$

A positive integer is twice another. The sum of the reciprocals of the two positive integers is \(3 / 12\). Find the two integers.

Simplify. (Assume all denominators are nonzero.) $$ 7854 $$

Translate the following sentences into a mathematical formula. The extension of a hanging spring, \(d\), is directly proportional to the weight, \(w,\) attached to it.

Multiply. (Assume all denominators are nonzero.) $$ -5 x 3 y \cdot y 225 x $$

Simplify. $$ x y-3 y $$

A positive integer is twice another. The difference of the reciprocals of the two positive integers is \(1 / 8\). Find the two integers.

Simplify. (Assume all denominators are nonzero.) $$ 103209 $$

Translate the following sentences into a mathematical formula. An automobile's breaking distance, \(d\), is directly proportional to the square of the automobile's speed, \(v\).

Evaluate for the given set of \(x\) -values. $$ 1 x+9 ;\\{-10,-9,0\\} $$

Solve. $$25 x-1 x=310$$

Simplify. $$ 4 x-3+6 x-3 $$

A positive integer is twice another. The difference of the reciprocals of the two positive integers is \(1 / 18\). Find the two integers.

Translate the following sentences into a mathematical formula. The volume, \(V\), of a sphere varies directly as the cube of its radius, \(r\).

Evaluate for the given set of \(x\) -values. $$ x+6 x-5 ;\\{-6,0,5\\} $$

Multiply. (Assume all denominators are nonzero.) $$ 16 a 47 b 2 \cdot 49 b 32 a 3 $$

Solve. $$12 x+1=5$$

A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is \(5 / 12,\) then find the two integers.

Simplify. (Assume all denominators are nonzero.) $$ 2356 $$

Translate the following sentences into a mathematical formula. The volume, \(V\), of a given mass of gas is inversely proportional to the pressure, \(p\), exerted on it.

State the restrictions to the domain. $$ 5 x $$

Solve. $$33 x-1+4=5$$

A positive integer is 2 more than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is \(17 / 35,\) then find the two integers.

Simplify. (Assume all denominators are nonzero.) $$ 74143 $$

Translate the following sentences into a mathematical formula. The intensity, \(I\), of light from a light source is inversely proportional to the square of the distance, \(d\), from the source.

Evaluate for the given set of \(x\) -values. $$ 9 \times 2-1 x-7 ;\\{0,1 / 3,7\\} $$

State the restrictions to the domain. $$ 1 x(3 x+1) $$

Multiply. (Assume all denominators are nonzero.) $$ x+102 x-1 \cdot x-2 x+10 $$

Solve. $$2 x-3 x+5=2 x+5$$

Simplify. $$ 2 x-9+x-11 x-9 $$

The sum of the reciprocals of two consecutive positive even integers is \(11 / 60\). Find the two even integers.

Simplify. (Assume all denominators are nonzero.) $$ \begin{array}{ll} 1-32 & 54-13 \end{array} $$

Translate the following sentences into a mathematical formula. Every particle of matter in the universe attracts every other particle with a force, \(F\), that is directly proportional to the product of the masses, \(m_{1}\) and \(m_{2}\), of the particles and inversely proportional to the square of the distance, \(d\), between them.

State the restrictions to the domain. $$ x+2 x 2-25 $$

Solve. $$5 \times 2 x-1=x-12 x-1$$

Simplify. $$ y+22 y+3-y+32 y+3 $$

The sum of the reciprocals of two consecutive positive odd integers is \(16 / 63\). Find the integers.

Simplify. (Assume all denominators are nonzero.) $$ 12-512+13 $$

State the restrictions to the domain. $$ x-1(x-1)(2 x-3) $$

Solve. $$5 x-7=6 x-9$$

Simplify. $$ 2 x-34 x-1-x-44 x-1 $$

The difference of the reciprocals of two consecutive positive even integers is \(1 / 24\). Find the two even integers.

Simplify. (Assume all denominators are nonzero.) $$ 1+321-14 $$