Solving One-Variable Equations with Letter Coefficients
Grade 9 students in California Reveal Math Algebra 1 learn to solve equations with letter coefficients by treating those letters as nonzero constants and applying the same properties of equality. If ax=b where a≠0, then x=b/a. Students solve equations like ax+3=15 (x=12/a), 3x-b=9 (x=(9+b)/3), and kx+2=mx+8 where factoring gives (k-m)x=6, so x=6/(k-m) when k≠m. This skill is especially valuable in science and applied math where formulas contain multiple constants alongside a single unknown.
Key Concepts
When a one variable equation contains a letter coefficient (a constant represented by a letter, such as $a$, $b$, or $k$), solve for the variable using the same properties of equality as with numeric coefficients. Isolate the variable by treating the letter coefficient as you would any nonzero number.
If $ax = b$ where $a \neq 0$, then: $$x = \frac{b}{a}$$.
Common Questions
What is a letter coefficient in an equation?
A letter coefficient is a constant represented by a letter — such as a, b, or k — that is not the variable being solved for. It represents a fixed but unspecified value.
How do you solve ax+3=15 for x?
Subtract 3 from both sides: ax=12. Divide both sides by a (where a≠0): x=12/a.
How do you solve 3x-b=9 for x?
Add b to both sides: 3x=9+b. Divide by 3: x=(9+b)/3.
How do you solve kx+2=mx+8 for x?
Subtract mx from both sides: kx-mx=6. Factor: (k-m)x=6. Divide by (k-m) where k≠m: x=6/(k-m).
Where is this skill used in real life?
In science and applied math, formulas often contain multiple constants alongside a single unknown. Solving for that unknown requires treating all other letters as constants and isolating the variable.
Which unit covers equations with letter coefficients?
This skill is from Unit 1: Using Expressions and Equations in California Reveal Math Algebra 1, Grade 9.