All kinds of algebra math
Introduction to all kinds of algebra math:-
In this article we are going to discuss about the all kinds of algebra math concept. Mainly algebra classified by three different types in math. The types are algebra 1, algebra 2, and pre-algebra. Here algebra 1, algebra 2, and pre-algebra chapters also show on this article. All kind of algebra math related problems show on below. And this article helps to improve your math algebra skills also.
Chapters for all kinds of algebra math:-
• Equations and Inequalities
• Linear Relationships and Functions
• Systems of Linear Equations and Inequalities
• Matrices and Matrix Operations
• Quadratic Equations
• Polynomial Functions
• Rational Expressions, Equations and Exponents
• Exponential and Logarithmic Functions
• Sequences and Series
• Trigonometry
• Trigonometric Identities and Graphs and Formulas
• Quadratic Relations/Analytic Geometry.
• Simplify Algebraic Expressions
• Operations with polynomials
• Simplify the degree and synthetic division
• Exponential expressions operation
• Fractions and then roots radicals and absolute values
• Factoring and increasing expressions and then consequence LCM and GCF
• Operation through complex number rationalizes complex denominator solving linear, quadratic and many extra equation and inequality comprise basic logarithmic and exponential equation.
• A system of two and three linear equation include Cramer's rule
• Graphing curve line, parabola, hyperbola, circle, ellipse, equation and inequality solution and graphing general function.
• Operation with function is composition, inverse, range, domain and simplifying logarithm.
• Essential geometry and trigonometry manipulative trig functions, right triangle
• Arithmetic and other pre-algebra topic is ratio, proportion, measurement.
Example all kinds of algebra math problems:-
All kinds of algebra math problem 1:-
Solve –3(5a + 4) + 7(3a – 1) = –43
Solution:-
–3(5a + 4) + 7(3a – 1) = –43 Original equation
–15a – 12 + 21a – 7 = –43 Distributive also replacement Properties
6a – 19 = –43
6a = –24 Addition and Substitution Properties
a = –4 Division and Substitution Properties
All kinds of algebra math problem 2:-
10 – |2a + 7| if a = –1.5.
Solution:-
10 – |2a + 7| = 10 – |2 (–1.5) + 7| Replace with –1.5.
= 10 – |–3 + 7| Simplify 2(–1.5) first
= 10 – |4| Add –3 and 7.
= 10 – 4 |4| = 4
= 6 Subtract.
All kinds of algebra math problem 3:-
Find the two methods to solve x2 + 12x = -20.
Solution:-
x2 + 12x = -20 Original equation
x2 + 12x + 20 = -20 + 20 Add 20 to each side.
x2 + 12x + 20 = 0 Simplify.
Method 1:-
For this equation, a = 1, b = 12, and c = 20.
x = `((-b)+-sqrt(b^2-(4*a*c)))/(2(a))` Quadratic Formula
=`((-12)+-sqrt((12^2 -(4(1) (20)))))/(2 (1))` a = 1, b = 12, and c = 20
`= (( -12) +- sqrt((144 - 80)))/(2)` Multiply.
`= ((-12)+- (sqrt64))/(2)` subtract.
=` (-12+- 8)/2 ` Take the square root of 64.
x `= (-12- 8)/2`
= -10
x `= (-12+ 8)/2`
= -2
Method 2:-
x2 + 12x + 20 = 0 Original equation
(x + 10)(x + 2) = 0 Factor x2 + 12x + 20.
x + 10 = 0 or x + 2 = 0 Zero Product Property
= -10 = -2 Solve.
The solution set is {-10, -2}.
In this article we are going to discuss about the all kinds of algebra math concept. Mainly algebra classified by three different types in math. The types are algebra 1, algebra 2, and pre-algebra. Here algebra 1, algebra 2, and pre-algebra chapters also show on this article. All kind of algebra math related problems show on below. And this article helps to improve your math algebra skills also.
Chapters for all kinds of algebra math:-
• Equations and Inequalities
• Linear Relationships and Functions
• Systems of Linear Equations and Inequalities
• Matrices and Matrix Operations
• Quadratic Equations
• Polynomial Functions
• Rational Expressions, Equations and Exponents
• Exponential and Logarithmic Functions
• Sequences and Series
• Trigonometry
• Trigonometric Identities and Graphs and Formulas
• Quadratic Relations/Analytic Geometry.
• Simplify Algebraic Expressions
• Operations with polynomials
• Simplify the degree and synthetic division
• Exponential expressions operation
• Fractions and then roots radicals and absolute values
• Factoring and increasing expressions and then consequence LCM and GCF
• Operation through complex number rationalizes complex denominator solving linear, quadratic and many extra equation and inequality comprise basic logarithmic and exponential equation.
• A system of two and three linear equation include Cramer's rule
• Graphing curve line, parabola, hyperbola, circle, ellipse, equation and inequality solution and graphing general function.
• Operation with function is composition, inverse, range, domain and simplifying logarithm.
• Essential geometry and trigonometry manipulative trig functions, right triangle
• Arithmetic and other pre-algebra topic is ratio, proportion, measurement.
Example all kinds of algebra math problems:-
All kinds of algebra math problem 1:-
Solve –3(5a + 4) + 7(3a – 1) = –43
Solution:-
–3(5a + 4) + 7(3a – 1) = –43 Original equation
–15a – 12 + 21a – 7 = –43 Distributive also replacement Properties
6a – 19 = –43
6a = –24 Addition and Substitution Properties
a = –4 Division and Substitution Properties
All kinds of algebra math problem 2:-
10 – |2a + 7| if a = –1.5.
Solution:-
10 – |2a + 7| = 10 – |2 (–1.5) + 7| Replace with –1.5.
= 10 – |–3 + 7| Simplify 2(–1.5) first
= 10 – |4| Add –3 and 7.
= 10 – 4 |4| = 4
= 6 Subtract.
All kinds of algebra math problem 3:-
Find the two methods to solve x2 + 12x = -20.
Solution:-
x2 + 12x = -20 Original equation
x2 + 12x + 20 = -20 + 20 Add 20 to each side.
x2 + 12x + 20 = 0 Simplify.
Method 1:-
For this equation, a = 1, b = 12, and c = 20.
x = `((-b)+-sqrt(b^2-(4*a*c)))/(2(a))` Quadratic Formula
=`((-12)+-sqrt((12^2 -(4(1) (20)))))/(2 (1))` a = 1, b = 12, and c = 20
`= (( -12) +- sqrt((144 - 80)))/(2)` Multiply.
`= ((-12)+- (sqrt64))/(2)` subtract.
=` (-12+- 8)/2 ` Take the square root of 64.
x `= (-12- 8)/2`
= -10
x `= (-12+ 8)/2`
= -2
Method 2:-
x2 + 12x + 20 = 0 Original equation
(x + 10)(x + 2) = 0 Factor x2 + 12x + 20.
x + 10 = 0 or x + 2 = 0 Zero Product Property
= -10 = -2 Solve.
The solution set is {-10, -2}.