Solved Examples: One-Step Equations with Rational Numbers Grade 7

📚 Quick Study Guide

• ➕ To solve an equation, isolate the variable.
• ➖ Use inverse operations to undo operations performed on the variable.
• ➗ For addition, subtract from both sides. For subtraction, add to both sides.
• ✖️ For multiplication, divide both sides. For division, multiply both sides.
• 🔢 Remember, rational numbers include fractions and decimals!
• 💡 Always check your answer by substituting it back into the original equation.
• ⚖️ Maintain balance: Whatever you do to one side, you must do to the other!

Practice Quiz

1. What is the solution to the equation $x + \frac{1}{2} = \frac{3}{4}$?
   A) $\frac{1}{4}$
   B) $\frac{5}{4}$
   C) $1$
   D) $\frac{3}{2}$
2. Solve for $y$: $y - 2.5 = 5.0$
   A) 2.5
   B) 7.5
   C) -2.5
   D) -7.5
3. What value of $z$ satisfies the equation $\frac{z}{3} = -2$?
   A) 6
   B) -6
   C) $\frac{2}{3}$
   D) $-\frac{2}{3}$
4. Find the solution to $4w = -8.4$.
   A) 2.1
   B) -2.1
   C) 33.6
   D) -33.6
5. Solve for $a$: $a + \frac{2}{5} = -\frac{1}{5}$
   A) $\frac{3}{5}$
   B) $-\frac{3}{5}$
   C) $\frac{1}{5}$
   D) $-\frac{1}{5}$
6. What is the value of $b$ in the equation $b - (-3.2) = 6.4$?
   A) 3.2
   B) -3.2
   C) 9.6
   D) -9.6
7. Solve: $\frac{2}{3}c = 8$
   A) 12
   B) $\frac{16}{3}$
   C) 4
   D) $\frac{4}{3}$