Real-world applications of ax + b = c: Two-step equation examples for Grade 7.

📚 Quick Study Guide

• 🔢 Two-Step Equations: These equations require two operations (addition/subtraction and multiplication/division) to isolate the variable.
• ✏️ General Form: The standard form is $ax + b = c$, where $x$ is the variable, and $a$, $b$, and $c$ are constants.
• ➕ Solving Steps:
  1. Isolate the term with the variable by adding or subtracting the constant term ($b$) from both sides of the equation.
  2. Isolate the variable ($x$) by dividing both sides of the equation by the coefficient ($a$).
• 💡 Real-World Examples: Think about splitting costs, calculating discounts, or determining travel time – all great uses for two-step equations!

Practice Quiz

1. What is the value of $x$ in the equation $2x + 3 = 7$?
   1. $x = 1$
   2. $x = 2$
   3. $x = 5$
   4. $x = 20$
2. Sarah bought 3 notebooks and a pen for $10. The pen cost $1. What was the cost of each notebook?
   1. $2
   2. $3
   3. $4
   4. $5
3. Solve for $x$ in the equation $5x - 8 = 12$.
   1. $x = 2$
   2. $x = 3$
   3. $x = 4$
   4. $x = 5$
4. A taxi charges a flat fee of $2 plus $0.50 per mile. If a ride costs $7, how many miles was the ride?
   1. 5 miles
   2. 7 miles
   3. 10 miles
   4. 14 miles
5. What is the solution to the equation $\frac{x}{2} + 1 = 5$?
   1. $x = 4$
   2. $x = 6$
   3. $x = 8$
   4. $x = 10$
6. John spent half of his money and then earned $5. He now has $15. How much money did he start with?
   1. $5
   2. $10
   3. $20
   4. $25
7. Solve for $x$: $4x + 6 = 22$
   1. $x = 2$
   2. $x = 3$
   3. $x = 4$
   4. $x = 5$