Algebra chapter 2 solving equations
what is the formula for perimeter of a rectangle?
P = 2l + 2w p = perimeter l = length w = width
what properties do you use to solve two step equations?
properties of equality and inverse operations.
how do you solve a two step equation?
1. identify the operations 2. undo them in reverse order of operations
what is the formula for area of a triangle?
A = ½×b×h a = area b = base h = height
Addition Property of Equality
If you add the same number to each side of an equation, the two sides remain equal. If a=b, then a+c=b+c
Division Property of Equality
If you divide each side of an equation by the same nonzero number, the two sides remain equal. if a=b, then a/c=b/c
Multiplication Property of Equality
If you multiply each side of an equation by the same nonzero number, the two sides remain equal. if a=b, then ac=bc
Subtraction Property of Equality
If you subtract the same number from each side of an equation, the two sides remain equal. if a=b, then a-c=b-c
How can you make this equation easier to solve? -8(2x-1) = 36
Remove the grouping symbols by using the distributive property
how do you solve an equation with variables on both sides?
To solve equations with variables on both sides, you can use properties of equality and inverse operations to write a series of simpler equivalent equations.
Inverse operations
Undoes another operation
why isn't -t = -5 a final solution to an equation?
When you solve for a variable the coefficient must be 1, not negative 1. -t is -1t. The final solution would be t = 5
what is the formula for area of a rectangle?
a = lw a = area l = length w = width
what is the formula for area of a circle?
a = πr² a = area r = radius
Literal equation
an equation that involves two or more variables
what is an identity?
an equation that is true for every possible value of the variable. For example x+1=x+1. An equation has no solution if there is no value of the variable that makes the equation true. For example x+1=x+2 has no solution. If the equation is true then there are infinitely many solutions.
isolate
to solve an equation you have to get the variable with a coefficient of 1 alone on one side of the equation.
What are the steps for solving equations?
1. Use the distributive property to remove any grouping symbols. Use properties of equality to clear decimals and fractions. 2. Combine like terms on each side of the equation 3. Use the properties of equality to get the variable terms on one side of the equation and the constants on the other 4. Use the properties of equality to solve for the variable 5. Check your solution in the original equation
formula
an equation that states a relationship among quantities. Formulas are special types of literal equations.
why do we multiply a fraction by its reciprocal?
because a fraction times its reciprocal equals 1. 1/3 x 3/1 = 1
what is the formula for the circumference of a circle?
c = 2πr c = circumference r = radius
what is the formula for temperature conversion?
c = 5/9(f-32) c = degrees selcius f = degrees Fahrenheit
what is the formula for distance traveled?
d = rt d = distance r = rate t = time
equivalent equations
equations that have the same solution
what equations are used in this equation? 2x+3 = 15
multiplication and addition. you can undo the addition first by subtracting and then the multiplication by division
how do you solve a multi-step equation?
you form a series of simpler equivalent equations. To do this, use the properties of inverse operations, and properties of real numbers. You use the properties until you isolate the variables.
