Solving with Negative Coefficients
Solve equations with negative coefficients in Grade 9 algebra. Divide both sides by the negative coefficient to isolate the variable, reversing inequality signs when working with inequalities.
Key Concepts
Property To solve a two step equation with a negative coefficient, use the same inverse operations to isolate the variable. Remember that dividing by a negative number is the final step to find the solution.
Examples To solve $8 = 5m + 6$, first subtract $6$ from both sides to get $2 = 5m$. Then divide by $ 5$ to find $m = \frac{2}{5}$. To solve $ 10 = 2x + 12$, first subtract $12$ from both sides to get $ 22 = 2x$. Then divide by $ 2$ to find $x = 11$.
Explanation Don't let a negative sign spook you! Just follow the reverse order of operations as always. Undo addition or subtraction first. The most important part is the final step: when you divide to isolate the variable, you must divide by the entire negative coefficient, including its negative sign, to solve correctly.
Common Questions
How do you solve an equation with a negative coefficient?
Divide both sides by the negative coefficient to isolate the variable. For -5x = 20, divide by -5: x = -4. For inequalities, also reverse the inequality sign.
What is the difference between solving equations and inequalities with negative coefficients?
For equations, divide by the negative coefficient — the equals sign stays. For inequalities, divide AND reverse the inequality direction (< becomes >, etc.).
How do you solve -3x + 7 = 1?
Subtract 7: -3x = -6. Divide by -3: x = 2. Check: -3(2) + 7 = -6 + 7 = 1. Correct.