Test yourself: Solving algebraic equations with negative x-terms.

📚 Quick Study Guide

🔢 Isolating the Variable: The goal is always to get 'x' by itself on one side of the equation. Remember, what you do to one side, you MUST do to the other! ⚖️ Dealing with Negative Coefficients: If you have $-x = 5$, multiply (or divide) both sides by -1 to get $x = -5$. This works because $-1 * -x = x$. ➕ Adding to Both Sides: If you have $5 = 2 - x$, add 'x' to both sides to eliminate it from the right: $5 + x = 2$. Then, isolate 'x' by subtracting 5 from both sides: $x = 2 - 5$, so $x = -3$. ➗ Dividing by Negative Coefficients: If you have $-3x = 12$, divide both sides by -3: $x = \frac{12}{-3}$, which simplifies to $x = -4$. 💡 Checking Your Work: Always plug your solution back into the original equation to make sure it's correct! This is the BEST way to avoid mistakes. 📝 Combining Like Terms: If the equation is complicated, simplify by combining like terms on each side before trying to isolate 'x'.

Practice Quiz

1. What is the value of $x$ in the equation $5 - x = 12$?
   1. $A) x = 7$
   2. $B) x = -7$
   3. $C) x = 17$
   4. $D) x = -17$
2. Solve for $x$: $-x + 3 = -4$
   1. $A) x = 7$
   2. $B) x = -7$
   3. $C) x = 1$
   4. $D) x = -1$
3. Find the value of $x$ in the equation: $2x + 7 = -x - 2$
   1. $A) x = 3$
   2. $B) x = -3$
   3. $C) x = -1/3$
   4. $D) x = -9$
4. What is the solution to the equation $-3x - 5 = 4$?
   1. $A) x = 3$
   2. $B) x = -3$
   3. $C) x = -1/3$
   4. $D) x = -9$
5. Solve for $x$: $8 - 2x = 14$
   1. $A) x = 3$
   2. $B) x = -3$
   3. $C) x = 11$
   4. $D) x = -11$
6. Find $x$ if $-(x - 3) = 7$
   1. $A) x = 4$
   2. $B) x = -4$
   3. $C) x = 10$
   4. $D) x = -10$
7. What is the value of $x$ in the equation $5x + 9 = 2x - 3$?
   1. $A) x = -4$
   2. $B) x = 4$
   3. $C) x = -1$
   4. $D) x = 1$