Solving Equations with Monomial Distribution
Solving equations with monomial distribution is a Grade 9 Algebra 1 skill in California Reveal Math (Unit 9: Polynomials). Apply the distributive property first — expanding all parentheses — then combine like terms and isolate the variable. For 3(2x + 5) = 33: distribute to get 6x + 15 = 33, subtract 15, then divide by 6 to get x = 3. When both sides need distribution, as in 2(3x+4) = 5(x-1), distribute both sides first before collecting variable terms.
Key Concepts
To solve an equation involving monomial polynomial multiplication, apply the Distributive Property on each side first, then combine like terms, and finally isolate the variable using inverse operations:.
$$a(bx + c) = d \;\Longrightarrow\; abx + ac = d \;\Longrightarrow\; x = \frac{d ac}{ab}$$.
Common Questions
How do you solve 3(2x + 5) = 33?
Distribute: 6x + 15 = 33. Subtract 15: 6x = 18. Divide by 6: x = 3. Always distribute first before applying inverse operations.
How do you solve -4(x - 3) = 20?
Distribute: -4x + 12 = 20. Subtract 12: -4x = 8. Divide by -4: x = -2. Note that -4 times -3 gives +12 in the distribution step.
How do you solve 2(3x + 4) = 5(x - 1)?
Distribute both sides: 6x + 8 = 5x - 5. Subtract 5x: x + 8 = -5. Subtract 8: x = -13. Each side must be fully distributed before collecting terms.
What is the correct order of steps for these equations?
Step 1: distribute the monomial across all terms in parentheses. Step 2: combine like terms on each side. Step 3: move variable terms to one side. Step 4: divide by the coefficient to isolate the variable.
What happens if you skip the distribution step?
Attempting to isolate the variable before distributing leads to an incorrect equation. For 3(2x+5) = 33, treating it as 3*2x + 5 = 33 is wrong. You must distribute 3 to both 2x and 5 first.