Solve for k (k+1)/2+(k+3)/4=1/2
The question provided is a linear algebraic equation involving a variable k. You are asked to solve for the value of k that makes the equation true. The equation includes fractions and the variable k is found in two different terms on the left side of the equation. To find the value of k, you would typically need to manipulate the equation using algebraic techniques to isolate k on one side of the equation.
Transform
Convert
Adjust each term to a denominator of
Scale
Multiply
Merge the numerators over the shared denominator.
Streamline the numerator.
Employ the distributive law.
Reposition
Execute the multiplication of
Combine
Cross-multiply by
Condense the equation.
Refine the left-hand side.
Eliminate the
Remove the
Express the simplified form.
Clarify the right-hand side.
Extract the
Isolate
Cancel out the
Rephrase the expression.
Determine the value of
Shift constants to the opposite side.
Subtract
Compute
Divide the equation by
Divide
Simplify the left-hand side.
Remove the
Simplify the right-hand side.
Divide
The problem involves solving a linear equation with fractions. The key knowledge points include:
Common Denominator: To combine fractions, they must have the same denominator. Multiplying by a form of one (e.g.,
Distributive Property: This property is used to simplify expressions, such as
Cross-Multiplication: When two fractions are set equal to each other, you can cross-multiply to eliminate the denominators.
Simplifying Equations: This involves canceling out common factors on both sides of the equation to isolate the variable.
Solving Linear Equations: The goal is to isolate the variable (in this case,
Understanding these concepts is crucial for solving linear equations and working with algebraic expressions involving fractions.