Solving Linear Equations with 1 variable – Review – Tutorial and Practice Questions

Linear equations with 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, 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.

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

 

 

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

 

 

 

 

 

 

 

 

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