Use this chart to quickly identify the correct inverse operation needed to solve for x.

The image you've uploaded is a helpful educational poster titled "Solving Equations", which demonstrates how to solve simple algebraic equations using inverse operations. Let's go through each example and explain the solution step by step.

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🔷 Top Left: Solving $ x + 23 = 90 $

Equation:
$$
x + 23 = 90
$$

Step:
To isolate $ x $, we undo addition by using subtraction (the inverse operation). Subtract 23 from both sides:

$$
x + 23 - 23 = 90 - 23
$$
$$
x = 67
$$

✔ Answer: $ x = 67 $

> 💡 Rule: *Undo addition with subtraction.*

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🔷 Top Right: Solving $ x - 12 = 74 $

Equation:
$$
x - 12 = 74
$$

Step:
To isolate $ x $, we undo subtraction by using addition (the inverse operation). Add 12 to both sides:

$$
x - 12 + 12 = 74 + 12
$$
$$
x = 86
$$

✔ Answer: $ x = 86 $

> 💡 Rule: *Undo subtraction with addition.*

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🔷 Bottom Left: Solving $ 4x = 48 $

Equation:
$$
4x = 48
$$

Step:
To isolate $ x $, we undo multiplication by using division (the inverse operation). Divide both sides by 4:

$$
\frac{4x}{4} = \frac{48}{4}
$$
$$
x = 12
$$

✔ Answer: $ x = 12 $

> 💡 Rule: *Undo multiplication with division.*

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🔷 Bottom Right: Solving $ \frac{x}{3} = 18 $

Equation:
$$
\frac{x}{3} = 18
$$

Step:
To isolate $ x $, we undo division by using multiplication (the inverse operation). Multiply both sides by 3:

$$
\frac{x}{3} \cdot 3 = 18 \cdot 3
$$
$$
x = 54
$$

✔ Answer: $ x = 54 $

> 💡 Rule: *Undo division with multiplication.*

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✔ Summary of Inverse Operations:

| Operation | Inverse Operation |
|----------|-------------------|
| Addition (+) | Subtraction (−) |
| Subtraction (−) | Addition (+) |
| Multiplication (×) | Division (÷) |
| Division (÷) | Multiplication (×) |

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🧠 Key Concept:

When solving equations, always perform the same operation on both sides to keep the equation balanced. The goal is to isolate the variable (usually $ x $) on one side.

This method works for linear equations in one variable and forms the foundation for more complex algebra.

Let me know if you'd like practice problems or want to see how this applies to multi-step equations!