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

Linear Equations with 1 Variable
Quick Review and Tutorial plus Practice Questions and Answer Key
Tutorial Practice Questions Answer Key
Quick Review and Tutorial – Solving Linear Equations
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
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Modified: December 18th, 2018 December 18th, 2018
Published: November 27th, 2014
2 Comments
thanks!! found this easy to answer
thanks alot for this preparation