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  • How to Solve Linear Equations in one variable – Tutorial and Practice Questions

How to Solve Linear Equations in one variable – Tutorial and Practice Questions

  • Posted by Brian Stocker MA
  • Date November 27, 2014
  • Comments 3 comments

Quick Review and Tutorial – How to Solve Linear Equations in One Variable

Linear equations in one variable x is an equation with the following form:

ax = b

where a and b are some real numbers. If a = 0 and b is different from 0, then the equation has no solution.

Let’s solve one simple example of a linear equation with one variable:

4x – 2 = 2x + 6

When we are given this type of equations, we are always moving variables to the one side of the equation, and real numbers to the other side of the equals sign. Always remember: if you are changing sides, you are changing signs. Let’s move all variables to the left, and real number to the right side:

4x – 2 = 2x + 6

4x – 2x = 6 + 2

2x = 8

x = 8/2

x = 4

When 2x goes to the left it becomes now -2x, and -2 goes to the right and becomes +2. After calculations, we find that x is 4, which is a solution of our linear equation.

Let’s solve a little more complex linear equation:

(2x – 6)/4 + 4 = x

2x – 6 + 16 = 4x

2x – 4x = -16 + 6

-2x = -10

x = -10/-2

x = 5

We multiply whole equation by 4, to lose the fractional line. Now we have a simple linear equation. If we change sides, we change the signs. At the end we do the final calculations.

Linear Equation in One Variable Practice Questions

1. Solve the linear equation:

-x – 7 = -3x – 9

a. -1
b. 0
c. 1
d
. 2

2. Solve the linear equation:

3(x + 2) – 2(1 – x) = 4x + 5

a. -1
b. 0
c. 1
d
. 2

3. Find the solution for the following linear equation:

 5x/2 = (3x + 24)/6

a. -1
b. 0
c. 1
d
. 2

4. If a and b are real numbers, solve the following equation:

(a+2)x-b = -2+(a+b)x

a. -1
b. 0
c. 1
d
. 2

5. Find the solution for the following linear equation:

1/(4x – 2) = 5/6

a. 0.2
b. 0.4
c. 0.6
d. 0.8

Answer Key

1. A -1

-x – 7 = -3x – 9
-x + 3x = -9 + 7
2x = -2
x = (-2):2
x = -1

2. C 1

3(x + 2) – 2(1 – x) = 4x + 5
3x + 6 – 2 + 2x = 4x + 5
5x + 4 = 4x + 5
5x – 4x = 5 – 4
x = 1

3.  D 2

12

 

 

 

 

 

 

 

 


4.  A -1

(a + 2)x – b = -2 + (a + b)x
ax + 2x – b = -2 + ax + bx
ax + 2x – ax – bx = -2 + b
2x – bx = -2 + b
(2 – b)x = -(2 – b)
x=-(2-b):(2-b)
x = -1

5.  D 0.8

1/(4x – 2) = 5/6 … We can cross multiply:
5(4x – 2) = 1 * 6 … Now, we distribute 5 to the parenthesis:
20x – 10 = 6 … We need x term alone on one side:
20x = 6 + 10
20x = 16 … Dividing both sides by 20:
x = 16/20 … Simplifying by 2 and having 10 in the denominator provides us finding the
decimal equivalent of x:
x = 8/10 = 0.8

Written by, Brian Stocker MA., Complete Test Preparation Inc.

Date Published: Thursday, November 27th, 2014
Date Modified: Tuesday, March 15th, 2022
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Brian Stocker MA

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November 27, 2014

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How to Solve Linear Equations with 2 Variables - Tutorial and Practice
November 27, 2014

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    3 Comments

  1. Jennifer
    March 31, 2018
    Reply

    thanks!! found this easy to answer

  2. Paul
    May 30, 2018
    Reply

    thanks alot for this preparation

  3. Charity ajema
    January 26, 2022
    Reply

    Wow good work

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