SOLVING EQUATIONS IN ONE VARAIABLE WORKSHEET

Solve the following equations

(1)  3x+4x  =  14             Solution

(2)  3x+4-6x  =  46         Solution

(3)  2x-5-x+7  =  12         Solution

(4)  2y-15+3y+3  =  24         Solution

(5)  3x+2(x-3)  =  -8         Solution

(6)  2(a+3)+3(a-2)  =  18         Solution

(7)  x + (x/2)  =  3         Solution

(8)  3x + (x/2)  =  15         Solution

(9) x - (x/3)  =  4         Solution

(10)  2x - (x/4)  =  14         Solution

(11)  When seven times a certain number is subtracted from 15, the result is -4. Find the number.

Solution

(12)  Four times a certain number, minus 5 is equal to 7 more than twice the number. What is the number ?

Solution

Answer Key

(1)  x  =  2

(2)  x  =  -17

(3)  x  =  10

(4)  y  =  36/5

(5)  x  =  -2/5

(6)  a  =  18/5

(7)  x  =  2

(8)  x  =  30/7

(9)  x  =  6

(10)  x  =  8

(11)  x  =  19/4

(12)  x  =  6

Solving each of the following rational equations

(1)  5/x - 1/3  =  1/x         Solution

(2)  1/6x2  =  1/3x- 1/x       Solution

(3)  3/x  =  2/(x + 4)            Solution

(4)  3/(x + 2) + 5  =  4/(x + 2)         Solution

(5)  2x/(x + 4) - 3  =  -12/(x + 4)         Solution

(6)  14/(2 – x)  =  2/x         Solution

(7)  2/(x - 4) + 2  =  6/(x - 4)          Solution

(8)  (x + 2)/(x + 1) - x  =  -6/(x + 1)         Solution

(9)   2 - 1/[x(x + 1)]  =  3/(x + 1)          Solution

(10)  x/(x + 2) +  2/(x2 + 5x + 6)  =  5/(x + 3)         Solution

Answer Key

(1)  x  =  12

(2)  x  =  1/6

(3)  x  =  -12

(4)  x  =  -9/5

(5)  x  =  0

(6)  x  =  1/16

(7)  x  =  6

(8)  x  =  -2√2  or  2√2

(9)  x  =  -1/2  or  1

(10)  x  =  4  or  -2

Word Problems

(1)  Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

(2)  Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers ?

(3)  If you subtract 1/2 from a number and multiply the result by 1/2, you get 1/8. What is the number.  

(4)  The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its width. What are the length and the width of the pool ?

(5)  The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 4 2/15 cm. What is the length of either of the remaining equal sides ? 

Solution

Answer Key

(1)  40 and 55

(2)  45 and 27

(3)  3/4

(4)  w  =  25 and l  =  52

(5)  1⅖ cm.

Solving algebraic equations with special cases

(1)  2x+2x+2  =  4x+2

(2)  3(x-1)  =  2x+9

(3)  2x+8  =  2(x+4)

(4)  2x-x+7  =  x+3+4

(5)  -2(x+1)  =  2x+5

(6)  Scott has 12 more 50 cents coins than 20 cent coins, and their total value is $10.20. How many 20 cent coins does Scott have?

(7)  At the supermarket a carton of juice costs $1.50 more than a bottle of milk. If 3 bottles of milk and 2 cartons of juice cost $8, how much does a carton of juice cost ?

Solution

Answer Key

(1)  infinitely many

(2)   one solution.

(3)  infinitely many

(4)  infinitely many

(5)  one solution

(6)  x  =  6

(7)  $2.50.

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