Solving for a Variable
Solve for a variable in Grade 9 algebra equations. Isolate the unknown using inverse operations across addition, subtraction, multiplication, and division in multi-step equations.
Key Concepts
Property As in an equation with one variable, use inverse operations and properties of equalities to solve for a specific variable in a literal equation.
Examples To solve $5x + 2y = 12$ for y: $2y = 12 5x$, so $y = \frac{12 5x}{2}$. To solve $P = 2l + 2w$ for w: $P 2l = 2w$, so $w = \frac{P 2l}{2}$. To solve $A = \frac{1}{2}bh$ for b: $2A = bh$, so $b = \frac{2A}{h}$.
Explanation Ready to be a variable detective? To solve for a specific letter, you need to isolate it! Use your trusty inverse operations—addition's arch nemesis is subtraction, and multiplication's is division. Your mission is to systematically move every other term and number to the other side of the equation, leaving your target variable standing alone and proud. It's all about undoing the math!
Common Questions
What does it mean to solve for a variable?
Solving for a variable means isolating it on one side of the equation using inverse operations, so the equation reads variable = value.
What is the correct order of inverse operations when solving for a variable?
Work in reverse order of PEMDAS: first undo addition or subtraction, then undo multiplication or division, then handle any exponents or parentheses.
How do you solve a formula for a specific variable?
Treat all other variables as constants and use inverse operations to isolate the target. For d = rt, divide both sides by r to get t = d/r.