Solve for y 2(y+4)-3x=0
Explanation of the question:
The problem provided is a linear algebraic equation with two variables, y and x. The goal is to solve for the variable y in terms of x. To do this, one would need to manipulate the equation to isolate y on one side, which will likely involve distributing the 2 into the parentheses where y is located, moving the term involving x to the other side, and dividing by the coefficient in front of y to solve for it explicitly.
$2 \left(\right. y + 4 \left.\right) - 3 x = 0$
Answer
Solution:
Step 1: Simplify the equation.
Apply the distributive property to expand the equation: $2(y + 4) - 3x = 0$ becomes $2y + 8 - 3x = 0$.
Perform the multiplication: $2 \times 4$ to get $8$.
Step 2: Isolate the variable $y$.
Subtract $8$ from both sides to move constants to the right: $2y - 3x = -8$.
Move the $x$ term to the right by adding $3x$ to both sides: $2y = 3x - 8$.
Step 3: Solve for $y$.
Divide the entire equation by $2$ to solve for $y$: $\frac{2y}{2} = \frac{3x}{2} - \frac{8}{2}$.
Simplify the equation by reducing fractions and dividing terms by $2$: $y = \frac{3x}{2} - 4$.
Knowledge Notes:
To solve an equation for a variable, you must isolate the variable on one side of the equation. Here are the steps and knowledge points involved in solving the given equation:
Distributive Property: This property allows you to multiply a single term and two or more terms inside a set of parentheses. For example, $a(b + c) = ab + ac$.
Moving Terms: To isolate a variable, you can move terms from one side of an equation to the other by performing the opposite operation (addition becomes subtraction, and vice versa) on both sides of the equation.
Simplifying Equations: This involves combining like terms and reducing fractions where possible to make the equation easier to solve.
Division: To solve for a variable that has a coefficient, divide the entire equation by that coefficient. This will leave the variable by itself on one side of the equation.
Latex Formatting: When writing mathematical expressions, Latex is used to format the expressions clearly and precisely. For example, $\frac{a}{b}$ represents the fraction of $a$ over $b$.
