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Section 1

Solving Linear Equations

Solve for the unknown, and then check your solution.$$x-7=9$$

Solve for the unknown, and then check your solution.$$x+11=5$$

Solve for the unknown, and then check your solution.$$5 x=0$$

Solve for the unknown, and then check your solution.$$2 w-7=5 w-7$$

Solve for the unknown, and then check your solution.$$4 w-3=w+5$$

Solve for the unknown, and then check your solution.$$7 m-4=3 m+12$$

Solve for the unknown, and then check your solution.$$9-5 r=4 r+11$$

Solve for the unknown, and then check your solution.$$3(4 w-5)=7(9-3 w)$$

Solve for the unknown, and then check your solution.$$3 p+2(5 p-6)=19+4(7-2 p)$$

Solve for the unknown, and then check your solution.$$2+3(5 t-9)=7 t-3(9-3 t)$$

Solve for the unknown, and then check your solution.$$5 n-3=2(9 n-7)+14-6 n$$

Solve for the unknown, and then check your solution.$$13-5 x+3(2 x-9)=12 x$$

Solve for the unknown, and then check your solution.$$\frac{2}{3} x=8$$

Solve for the unknown, and then check your solution.$$\frac{3}{5} y=9$$

Solve for the unknown, and then check your solution.$$\frac{5}{2} z=\frac{4}{3}$$

Solve for the unknown, and then check your solution.$$\frac{3}{4} w+2=w-\frac{1}{2}$$

Solve for the unknown, and then check your solution.$$\frac{3}{4} w-\frac{2}{3} w+\frac{1}{4}=\frac{1}{6} w+3$$

Solve for the unknown, and then check your solution.$$\frac{3}{5} y-\frac{3}{4}=\frac{1}{4} y+\frac{7}{10}$$

Solve for the unknown, and then check your solution.$$0.2 x-0.3(5-2 x)=0.4$$

Solve for the unknown, and then check your solution.$$0.35+0.24 x=0.2(5-3 x)$$

Solve for the unknown, and then check your solution.$$0.4 r-0.52(40-2 r)=100$$

Solve for the indicated variable.$$\text { For } x: 5 x-2 y=19$$

Solve for the indicated variable.$$\text { For } y: 5 x-2 y=19$$

Solve for the indicated variable.$$\text { For } x: a x+b y=c$$

Solve for the indicated variable.$$\text { For } y: a x+b y=c$$

Solve for the indicated variable.$$\text { For } C: F=9 / 5 C+32$$

Solve for the indicated variable.$$\text { For } h: V=\pi r^{2} h$$

Solve for the indicated variable.$$\text { For } b: A=1 / 2 h(a+b)$$

Solve for the indicated variable.$$\text { For } S: 1 / R=1 / S+1 / W$$

Today, Maria's age is 5 years less than twice Louie's age. In five years, the sum of their ages then will be 41. What are their present ages?

Mike is 5 years older then Joan. In ten years, the sum of their ages will be 57 . What are their present ages?

Alphonse took four examinations and his average on these four exams was 83. If his grades on the first three exams were 82,88 and $78,$ what grade did he get on the fourth exam?

The length of a rectangle is two feet less than three times its width. If the perimeter is 36 feet, what are the dimensions of the rectangle?

An isosceles triangle has a perimeter of 33 centimeters. If the equal sides are 6 centimeters less than twice the unequal side, what is the length of the two equal sides?

The sum of three consecutive integers is $96,$ find the three integers.

The sum of two consecutive odd integers is 15 more than the next odd integer. Find the three integers.

Boston and New York are approximately 280 miles apart. One train leaves Boston traveling towards New York at an average speed of 80 mph. Another train leaves New York at the same time traveling toward Boston at an average speed of 60 mph. (a) How long will it take them to meet. (b) How far has each train traveled when they meet?

Two cars leave a city traveling in the same direction. One travels at $60 \mathrm{mph}$ and the other at 45 mph. How long before the cars are 60 miles apart?

Two planes leave JFK airport at the same time, one flying north at $500 \mathrm{mph}$ and the other south at 600 mph. In how many hours will they be 4400 miles apart?

Two angles are said to be complementary if the sum of the measures of their angles is 90 degrees. If one angle is 15 degrees more than twice the other, what is the measure of the smaller angle?

Two angles are said to be supplementary if the sum of the measures of their angles is 180 degrees. If one angle is 30 degrees less than six times the other, what is the measure of the larger angle?

James has a collection of nickels and dimes which total to 5.15 dollar. If he has 5 fewer nickels than dimes, how many dimes has he?

The denominator of a fraction is 1 less than three times the numerator. If the numerator is increased by 1 and the denominator is decreased by 2 the resulting fraction is $1 / 2$. Determine the original fraction.

The numerator of a fraction is three less than the denominator. Tripling the numerator and quadrupling the denominator results in a fraction equal to $3 / 5$ Determine the original fraction.

6,000 dollar is invested for two years earning annual simple interest at $4 \% ;$ to what does it accumulate?

How long does it take 5,000 dollar to earn a total interest of 600 dollar if the annual simple interest rate is $4 \% ?$

What annual simple interest does a 10,000 dollar investment earn if it accumulates to 11,200 dollar after three years?