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Math

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  • Practice Solving Algebra Equations – Learn at your Own Pace

Practice Solving Algebra Equations – Learn at your Own Pace

  • Posted by Brian Stocker MA
  • Date October 11, 2012
  • Comments 25 comments

Algebra on Standardized Tests

Basic Algebra is a common subject for the following exams:

College Entrance, High School 

Nursing Entrance

See our tutorial on solving linear equations with 1 variable

More information and Algebra Tutorials

Wikipedia

Virtual Math Lab – Beginning Algebra 

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How to Study for a Math Test

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Practice your Algebra with a Free quiz

Algebra Practice Questions

 

1. 5x + 3 = 7x – 1. Find x

a. 1/3
b. ½
c. 1
d. 2

2. 5x + 2(x + 7) = 14x – 7. Find x

a. 1
b. 2
c. 3
d. 4

3. 12t – 10 = 14t + 2. Find t

a. -6
b. -4
c. 4
d. 6

4. 5(z + 1) = 3(z + 2) + 11 Solve for Z

a. 2
b. 4
c. 6
d. 12

5. The price of a book went up from $20 to $25. By how many percent did the price increase?

a. 5
b. 10
c. 20
d. 25

6. The price of a book decreased from $25 to $20. By how many percent did the price decrease?

a. 5
b. 10
c. 20
d. 25

7. After taking several practice tests, Brian improved the results of his GRE test by 30%. Given that the first time he took the test Brian had answered 150 questions correctly, how many correct answers did he answer in the second test?

a. 105
b. 120
c. 180
d. 195

 

8.  A number is increased by 2 and then multiplied by 3. The result is 24. What is this number?

a. 4
b. 6
c. 8
d.  10

9. My father’s age divided by 5 is equal to my brother’s age divided by 3. My brother is 3 years older than me. My father’s age is 3 less than 2 times my age. How old is my father?

a. 34
b. 45
c. 56
d. 61

10.  (x – 2) / 4 – (3x + 5) / 7 = – 3, x = ?

a. 6
b. 7
c. 10
d. 13

11.  1 / (1 + 1 / (1 – 1/x)) = 4, x = ?

a. – 3/4
b. 3/7
c. 4/7
d. 3/4

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Answer Key

1. D
5x + 3 = 7x – 1
now collect like terms
3 + 1 = 7x – 5x
every time you move something it changes signs
4 = 2x anything multiplied is divided on the other side and vice versa
4/2 = x
2 = x

2. C
5x + 2(x + 7) = 14x – 7
5x + 2x + 14 = 14x – 7
7x + 14 = 14x – 7
7x – 14x = -14 – 7
-7x = -21
x = 3

3. A

4. C
5(z + 1) = 3(z + 2) + 11. Z=?
5z + 5 = 3z + 6 + 11
5z + 5 = 3z + 17
5z = 3Z + 17 – 5
5z – 3z = 12
2z = 12
z = 6

5. D
The price increased from $20 to $25 ($5) so the question is 5 is what percent of 20. Or, 5/20 = x/100 ; 500/20 = 25%

6. C

7. D
The first time, Brian answered 150 questions correctly and the second time he answered 30% more correctly, so,
150 + (30/100 * 150) ; 30% of 150 = 45, or (30 * 150)/100
so 150 + 45 = 195

8. B

Let us call this number by x:

This number is increased by 2: x + 2

Then, it is multiplied by 3: 3(x + 2)

The result is 24: 3(x + 2) = 24 … Solving this linear equation, we obtain the value of the number:

x + 2 = 24 / 3

x + 2 = 8

x = 8 – 2

x = 6

9. B

My age: x

My brother is 3 years older than me: x + 3

My father is 3 less than 2 times my age: 2x – 3

My father’s age divided by 5 is equal to my brother’s age divided by 3: (2x – 3) / 5 = (x + 3) / 3

By cross multiplication:

5(x + 3) = 3(2x – 3)

5x + 15 = 6x – 9

x = 24

My father’s age: 2.24 – 3= 48 – 3 = 45

10. C

There are two fractions containing x and the denominators are different. First, let us find a common denominator to simplify the expression. The least common multiplier of 4 and 7 is 28. Then,

7(x – 2) / 28 – 4(3x + 5) / 28 = – 3.28 / 28 … Since both sides are written on the denominator 28 now, we can eliminate them:

7(x – 2) – 4(3x + 5) = – 84

7x – 14 – 12x – 20 = – 84

– 5x = – 84 + 14 + 20

– 5x = – 50

x = 50/5

x = 10

11. B

We can follow outside to inside method to solve this type of problems. x is in the inner part of this fraction; then, we need to narrow the circle to reach x:

1 / (1 + 1 / (1 – 1/x)) = 4

This means that (1 + 1 / (1 – 1/x)) is equal to 1/4. Then,

1 + 1 / (1 – 1/x) = 1/4

1 / (1 – 1/x) = 1/4 – 1

1 / (1 – 1/x) = – 3/4

This means that 1 – 1/x = – 4/3. Then,

1 – 1/x = – 4/3

1 + 4/3 = 1/x

1/x = 7/3

So, x = 3/7.

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    25 Comments

  1. Timothy Crouse
    January 21, 2014
    Reply

    I need to know how to do the formula in order to pass algebra to get accepted into a practical nursing program. Also, I need to learn basic mathematics.

    • James R.
      September 7, 2015
      Reply

      you can search the formulas for basic allgebra online

    • Helpful Person
      February 4, 2017
      Reply

      In order to solve it you have to look at the two sides separated by the equal sign then combine like terms after you add or subtract from both sides so a variable(s) is on one side and the numbers are on one side then if they have a common factor divide them by the smallest of the two then you will get your answer.

      • alana
        August 6, 2019
        Reply

        Hello Will you please show me how you break this problem down in order to solve it. I read what you wrote and it makes sense but i’m visual and need to see it broken down as well as explained.
        1. 5x + 3 = 7x – 1. Find x
        is it 8x = 6x
        4x divided by 3x x = .3333 or 1/3
        haha! help. thanks.

        a. 1/3
        b. ½
        c. 1
        d. 2

        • cal
          October 27, 2019
          Reply

          5x+3=7x-1
          subtract the 5x from 7x to move it to the other side to make equation 3=2x-1
          now add the 1 to the 3 to move it to the other side to make the equation 4=2x
          now subtract the 2 from the x to isolate the x and make the equation 4/2=x
          4/2=2
          X=2

        • Abigale kirsten
          October 27, 2019
          Reply

          No, You cannot add and subtract number just because they are next to each other. You must align same groups with each other.
          5x needs ti be joined with 7x, +3 needs to be joined with -1.
          However, when we align and group them, it means switching them from theyre placements where they will cross the equal sign.
          The rule is, anything that has to cross the equal sign in order to group numbers will automatically have their plus and minus signs changed.
          Therefore, this is how itll look.

          5x + 3 = 7x – 1. Find X,
          5x – 7x = – 1- 3
          -2x = + 4
          x = +4 / +2
          x = +6

          Note: 5x – 7x became -2x, as 7 is the bigger number out of the two that are being subtracted, therefore the result will adopt the minus sign from the bigger number.
          Note: -1 -3 became +4 because whenever you put minus and minus together, they become a positive. Those are the rules of Algebra,

          • Mehmet Yilmaz
            December 20, 2019

            Sorry Abigale Kirsten, but that isn’t correct, -1-3 isn’t equal to +4, because that only happens in multiplication, what will happen here is it will equal -4 because -1-1 is equal to -2, if anyone disagrees please check it via a calculator.
            Coming to the question, 5x + 3 = 7x – 1. Find X
            We take -1 to the other side making it positive
            5x+3+1=7x
            This equals to
            5x+4=7x
            Here we now take 5x to the other side
            4=7x-5x
            which equals to
            4=2x
            we divide both sides by 2
            And the answer is
            x=2

            I anyone doubts this please use google or a specialized calculator to check it.

          • Brian Stocker
            December 20, 2019

            thanks for the great explanation – better than mine!

          • wee
            February 29, 2020

            Im in 7th grade and I finished this problem in 20 sec and the answer is x = 2. step by step is 5x+3=7x-1 —> you minus 5x on both sides because it is the smaller variable and you get 3 = 2x-1. The opposite of subtraction is addition, we need to isolate the x variable by getting rid of the -1 so we do (-1) + 1 is 0 and we do it on both sides of the equal sign. then the equation would be 3 + 1 = 2x -1 +1. After that, the equation would look like this: 4 = 2x then we divide the variable on both sides so it would be 4/2 = 2/2, —> then 2=x

    • Sultan
      March 9, 2020
      Reply

      Wow this is good plus who can solve this
      7(x+4)-2[x-3(5+x)]=2/3(x-6)
      a. 6
      b.7
      c.-6
      d.3

      • Anonymous
        October 3, 2020
        Reply

        is it c

  2. Sandra
    January 24, 2017
    Reply

    Could you explain 4 like you did 1?

    • Brian
      January 24, 2017
      Reply

      OK updated solution for #4 – will get to the others soon!

  3. Tammy kent
    March 23, 2017
    Reply

    for question 2. I keep getting 2 for an answer. Can you please show the breakdown on the solution.

    • Brian
      March 23, 2017
      Reply

      ok!

  4. Odey Grace
    June 1, 2017
    Reply

    Please no I need explanation for no 7

    • Sunny
      June 4, 2018
      Reply

      150 × .30 = 45 + 150 = 195

      • Regis Finn
        June 30, 2020
        Reply

        Or to make it easier, multiple by 1.30 instead of .30

  5. Tahmina Hossain
    February 8, 2018
    Reply

    Answer for question 5 should be c. 20%

    • Brian
      February 9, 2018
      Reply

      The price increased from $20 to $25 ($5) so the question is 5 is what percent of 20.  Or, 5/20 = x/100  ;  500/20 = 25%

  6. leilei
    March 7, 2019
    Reply

    THIS IS TOOOOOOO HARD IM NEVER DOING ALGEBRA AGAIN BUT I DID GET THE CORRECT ANSWER THO

    • chris
      June 29, 2019
      Reply

      or x/150=1.3 because a 30% increase is really 130% or 1.3 so if you start with x/150=1.3 you solve for x by multiplying 150 and 1.3 so the equations becomes 150*1.3=x so solving for x X=195

  7. leslee smith
    April 30, 2020
    Reply

    can you please show me how to breakdown and solve number 11?

  8. Ashu
    July 1, 2020
    Reply

    Can u do other questions around square and cubing digits and dividing and multiplying using algebraic equations

  9. Sarah
    September 21, 2020
    Reply

    There are a number of 7L tins of paint and 5L tins of paint. How many tins of each do we need to make up 102L of paint?
    How is this worked out in an algebra equation?

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