Introduction:
In this article, we are going to study math for middle school by online test. This is much helpful for the students to study the middle school math. Middle school online math test covers the following topics such as arithmetic operations, algebra, geometry and measurements. Online study for middle school math provides the step by step solutions to all problems. Online middle school math test to study is very interactive and fun to learn for the students. I like to share this Linear Equation Calculator with you all through my article.
Linear equation problem solving:
Methods of solving liner equations in one variable:
Add the same number on both the sides of the equation.
Subtract the same number from the both sides of the equation.
Multiply the both sides of the equation by the same number (other than zero)
Divide the both sides of the equation by the same number (other than zero).
Statements with problems:
The unknown quantities may be symbolized by say x,y,z
Translate the statements of the problem word by word (step by step) into mathematical statements, to the extent it is possible.
Look for the quantities, which are equal and write the equation by writing appropriate expressions for these quantities.
Solve the equation for the unknown.
Check, whether the solution satisfies the conditions given in the problem
Example problems:
Example 1: Solve: 1/3 x – 5/2=6
Solution: 1/3 x -5/2= 6
Or 3x -4x +10 = 2x + 6 – 8
or -x +10 = 2x – 2
Now by transposing 2 x from right side to the left side we have.
- x + 10 - 2x = -2
or - 3x = - 2 - 10
or - 3x = - 12
-1/3 - 3x =-1/3-12
or x = 4
Example 2: Solve : 3x -2(2x - 5) = 2 (x + 3) - 8
Solution : Here the unknown quantity x appears on both sides. Thus before transposing we simplify the expressions of both the sides.
Thus, 3x - 2 (2x - 5) = 2(x + 3) -8
Thus x =9/8is the solution of the equation
Check: L.H.S. = 0.6x + 4/8
= 0.6 x 9/8 + 4/5
= 54/80 +4/5
= 27/40 + 4/5 = 59 /40
R.H.S. = 0.28 x + 1.16
= 0.28 ×9/8 + 116/100
=63/200 + 116/100
= 63 + 232/200
= 295/200
=59/40
Thus L.H.S. = R.H.S., Therefore, x=9/8
Thus x = 4 is the solution of the equation Check : L.H.S.
= 3x - 2 (2x - 5)
= 3×4 - 2(2×4 - 5)
= 12 - 2 (8 - 5)
= 12 - 2 × 3
= 12 - 6 = 6
R.H.S. = 2 (x+3) 8
= 2 (4+3) - 8
= 14 - 8 = 6
L.H.S. = R.H.S.
Hence x = 4 is the correct solution. Having problem with systems of linear equations in two variables keep reading my upcoming posts, i will try to help you.
Practice problems:
Problem 1: Collect like terms and simplify the given expression: 10m^2 – 9m + 5m – 4m^2 – 7m + 8
Answer : 6m^2 – 11m + 8
Problem 2: The curved surface area of a right circular cylinder of height 14 cm is 88 cm^2. Find the radius of the base of the cylinder.
Answer : 1 cm
Problem 3: Curved surface area of a cone is 308 cm^2 and its slant (h) height is 14 cm. find the radius (r) of the base.
Answer : 7cm
Problem 4: Solve 2x +6 = 10
Answer: 2
In this article, we are going to study math for middle school by online test. This is much helpful for the students to study the middle school math. Middle school online math test covers the following topics such as arithmetic operations, algebra, geometry and measurements. Online study for middle school math provides the step by step solutions to all problems. Online middle school math test to study is very interactive and fun to learn for the students. I like to share this Linear Equation Calculator with you all through my article.
Linear equation problem solving:
Methods of solving liner equations in one variable:
Add the same number on both the sides of the equation.
Subtract the same number from the both sides of the equation.
Multiply the both sides of the equation by the same number (other than zero)
Divide the both sides of the equation by the same number (other than zero).
Statements with problems:
The unknown quantities may be symbolized by say x,y,z
Translate the statements of the problem word by word (step by step) into mathematical statements, to the extent it is possible.
Look for the quantities, which are equal and write the equation by writing appropriate expressions for these quantities.
Solve the equation for the unknown.
Check, whether the solution satisfies the conditions given in the problem
Example problems:
Example 1: Solve: 1/3 x – 5/2=6
Solution: 1/3 x -5/2= 6
Or 3x -4x +10 = 2x + 6 – 8
or -x +10 = 2x – 2
Now by transposing 2 x from right side to the left side we have.
- x + 10 - 2x = -2
or - 3x = - 2 - 10
or - 3x = - 12
-1/3 - 3x =-1/3-12
or x = 4
Example 2: Solve : 3x -2(2x - 5) = 2 (x + 3) - 8
Solution : Here the unknown quantity x appears on both sides. Thus before transposing we simplify the expressions of both the sides.
Thus, 3x - 2 (2x - 5) = 2(x + 3) -8
Thus x =9/8is the solution of the equation
Check: L.H.S. = 0.6x + 4/8
= 0.6 x 9/8 + 4/5
= 54/80 +4/5
= 27/40 + 4/5 = 59 /40
R.H.S. = 0.28 x + 1.16
= 0.28 ×9/8 + 116/100
=63/200 + 116/100
= 63 + 232/200
= 295/200
=59/40
Thus L.H.S. = R.H.S., Therefore, x=9/8
Thus x = 4 is the solution of the equation Check : L.H.S.
= 3x - 2 (2x - 5)
= 3×4 - 2(2×4 - 5)
= 12 - 2 (8 - 5)
= 12 - 2 × 3
= 12 - 6 = 6
R.H.S. = 2 (x+3) 8
= 2 (4+3) - 8
= 14 - 8 = 6
L.H.S. = R.H.S.
Hence x = 4 is the correct solution. Having problem with systems of linear equations in two variables keep reading my upcoming posts, i will try to help you.
Practice problems:
Problem 1: Collect like terms and simplify the given expression: 10m^2 – 9m + 5m – 4m^2 – 7m + 8
Answer : 6m^2 – 11m + 8
Problem 2: The curved surface area of a right circular cylinder of height 14 cm is 88 cm^2. Find the radius of the base of the cylinder.
Answer : 1 cm
Problem 3: Curved surface area of a cone is 308 cm^2 and its slant (h) height is 14 cm. find the radius (r) of the base.
Answer : 7cm
Problem 4: Solve 2x +6 = 10
Answer: 2
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