## How to Solve One Step Equations?

What is an Equation?

In mathematics, an equation is a statement that uses an equal sign (=) to assert that two algebraic expressions have the same value. The expression on the left of the equal sign is called the "Left Hand Side" (LHS), while the expression on the right is called the "Right Hand Side" (RHS) of the equation. Algebraic expressions within an equation can consist of constants, variables, and mixed expressions (variables with coefficients).

Properties of Equations

Equations have several important properties:

1. You can add or subtract the same number from both sides of an equation without affecting its validity. The equation will still hold true.
2. You can multiply or divide both sides of an equation by the same non-zero number without affecting its validity. The equation will still hold true.

Solving One-Step Equations

To solve a one-step equation, follow these steps:

1. Move the constant value to the other side of the equation by inverting its sign (i.e., if it's positive, make it negative, and vice versa).
2. Perform one mathematical operation (addition, subtraction, multiplication, or division) to isolate the variable and solve the equation.

Examples:

• $$x \ – \ 2 \ = \ 10 \ ⇒ \ x \ = \ 10 \ + \ 2 \ ⇒ \ x \ = \ 12$$.
• $$x \ – \ 7 \ = \ -14 \ ⇒ \ x \ = \ -14 \ + \ 7 \ ⇒ \ x \ = \ -7$$.
• $$7x \ = \ 10 \ ⇒ \ x \ = \ \frac{10}{7} \ ⇒ \ x \ = \ 1.42$$.
• $$2x \ – \ 4 \ = \ 10 \ ⇒ \ 2x \ = \ 10 \ + \ 4 \ ⇒ \ x \ = \ \frac{14}{2} \ = \ 7$$.
• $$3x \ – \ 21 \ = \ -14 \ ⇒ \ 3x \ = \ -14 \ + \ 21 \ ⇒ \ x \ = \ \frac{7}{3}$$ .
• $$4x \ = \ 92 \ ⇒ \ x \ = \ \frac{92}{4} \ ⇒ \ x \ = \ 23$$.
• $$9x \ – \ 2x \ + \ 5 \ = \ 10 \ ⇒ \ 7x \ = \ 10 \ - \ 5 \ ⇒ \ x \ = \ \frac{5}{7}$$ .
• $$x \ – \ 3x \ = \ -14 \ ⇒ \ -2x \ = \ -14 \ ⇒ \ x \ = \ \frac{-14}{-2} \ = \ 7$$.
• $$7x \ = \ -15 \ + \ 2x \ ⇒ \ 5x \ = \ -15 \ ⇒ \ x \ = \ \frac{-15}{5} \ = \ -3$$.

### Exercises for One Step Equations

1) $$x \ - \ 2 = 10$$$$\ \Rightarrow \$$

2) $$x \ - \ 5 = 3$$$$\ \Rightarrow \$$

3) $$x \ + \ 4 = 5$$$$\ \Rightarrow \$$

4) $$x \ + \ 2 = -2$$$$\ \Rightarrow \$$

5) $$x \ - \ 4 = 4$$$$\ \Rightarrow \$$

6) $$x \ - \ 4 = 11$$$$\ \Rightarrow \$$

7) $$x \ - \ 5 = -4$$$$\ \Rightarrow \$$

8) $$x \ - \ 2 = -3$$$$\ \Rightarrow \$$

9) $$x \ + \ 4 = -8$$$$\ \Rightarrow \$$

10) $$x \ + \ 4 = 6$$$$\ \Rightarrow \$$

1) $$x \ - \ 2 = 10$$$$\ \Rightarrow \ \color{red}{x = 10 \ + \ 2 = 12}$$
2) $$x \ - \ 5 = 3$$$$\ \Rightarrow \ \color{red}{x = 3 \ + \ 5 = 8}$$
3) $$x \ + \ 4 = 5$$$$\ \Rightarrow \ \color{red}{x = 5 \ - \ 4 = 1}$$
4) $$x \ + \ 2 = -2$$$$\ \Rightarrow \ \color{red}{x = -2 \ - \ 2 = -4}$$
5) $$x \ - \ 4 = 4$$$$\ \Rightarrow \ \color{red}{x = 4 \ + \ 4 = 8}$$
6) $$x \ - \ 4 = 11$$$$\ \Rightarrow \ \color{red}{x = 11 \ + \ 4 = 15}$$
7) $$x \ - \ 5 = -4$$$$\ \Rightarrow \ \color{red}{x = -4 \ + \ 5 = 1}$$
8) $$x \ - \ 2 = -3$$$$\ \Rightarrow \ \color{red}{x = -3 \ + \ 2 = -1}$$
9) $$x \ + \ 4 = -8$$$$\ \Rightarrow \ \color{red}{x = -8 \ - \ 4 = -12}$$
10) $$x \ + \ 4 = 6$$$$\ \Rightarrow \ \color{red}{x = 6 \ - \ 4 = 2}$$

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