How to Solve Two Step Equations

How to Solve Two Step Equations?

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Before solving two-step equations, let’s look at the definition of an equation first,

What is an Equation?

What is the definition of an equation? The term "equation" in mathematics refers to a statement that has the equal sign "=" in between two algebraic statements. Furthermore, the values of these two algebraic assertions are the same. The expression on the left is referred to as the "Left Hand Side" of the equation, whereas the expression on the right is referred to as the "Right Hand Side" of the equation, and vice versa. If the "Left Hand Side" of a mathematical equation equals the "Right Hand Side," then the equation is complete.
An equation contains algebraic expressions that contain both constants and variables, as well as a mixture of the two (variables with coefficients).

Types of Equations

There are three common types of equations: Linear, Quadratic, and Cubic.

Linear Equation: The standard form of a linear equation is $ax + by = 0$ . In this equation, $x$ and $y$ are variables, and a and b are constants.
Quadratic Equation: The standard form of a quadratic equation is $ax^2 + bx + c = 0$ , where $a ≠ 0$ . In this equation, $x$ is the variable, and $a, b,$ and $c$ are constants.
Cubic Equation: The standard form of a cubic equation is $ax^3 + bx^2 + cx + d = 0$ , where $a ≠ 0$ . In this equation, $x$ is the variable, and $a, b, c,$ and $d$ are constants.

Solving Two-Step Equations

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

Perform the inverse of addition or subtraction to simplify the equation. This typically involves moving the constant term to the other side of the equation by changing its sign (i.e., if it's positive, make it negative, and vice versa).
Further simplify the equation by performing the inverse of multiplication or division to isolate the variable and solve the equation.

Examples:

$2(x \ – \ 2) \ = \ 10 \ ⇒ \ 2x \ - \ 4 \ = \ 10 \ ⇒ \ 2x \ = \ 10 \ + \ 4 \ ⇒ \ 2x \ = \ 14 \ ⇒ \ x \ = \ \frac{14}{2} \ = \ 7$
$3(-x \ – \ 4) \ = \ 12 \ ⇒ \ -3x \ - \ 12 \ = \ 10 \ ⇒ \ -3x \ = \ 10 \ + \ 12 \ ⇒ \ -3x \ = \ 22 \ ⇒ \ x \ = \ \frac{-22}{3}$
$5(2x \ – \ 3) \ = \ 10 \ ⇒ \ 10x \ - \ 15 \ = \ 10 \ ⇒ \ 10x \ = \ 10 \ + \ 15 \ ⇒ \ 10x \ = \ 25 \ ⇒ \ x \ = \ \frac{25}{10} \ = \ \frac{5}{2}$
$7(-2x \ – \ x) \ = \ 10 \ ⇒ \ -14x \ – \ 7x \ = \ 10 \ ⇒ \ -21x \ = \ 10 \ ⇒ \ x \ = \ \frac{10}{-21} \ = \ -\frac{10}{21}$

Free printable Worksheets

Exercises for Two Step Equations

1) $3(x \ - \ 6) = 12$ $\ \Rightarrow \$

2) $4x \ - \ 16 = 20$ $\ \Rightarrow \$

3) $\frac{ 6x \ - \ 18}{7} = 36$ $\ \Rightarrow \$

4) $\frac{ 4x \ - \ 20}{6} = 52$ $\ \Rightarrow \$

5) $3x \ - \ 15 = -6$ $\ \Rightarrow \$

6) $2(x \ - \ 10) = 38$ $\ \Rightarrow \$

7) $2x \ - \ 6 = -2$ $\ \Rightarrow \$

8) $\frac{ 2x \ - \ 6}{5} = 14$ $\ \Rightarrow \$

9) $\frac{ 3x \ - \ 12}{4} = 42$ $\ \Rightarrow \$

10) $6(x \ - \ 12) = 72$ $\ \Rightarrow \$

Answers

$3(x \ - \ 6) = 12$

$\ \Rightarrow \ \color{red}{x \ - \ 6= \frac{12}{3}}$

$\ \Rightarrow \ \color{red}{ x = 4 \ + \ 6 = 10}$

$4x \ - \ 16 = 20$

$\ \Rightarrow \ \color{red}{x = \frac{20 \ + \ 16}{4} = 9}$

$\frac{ 6x \ - \ 18}{7} = 36$

$\ \Rightarrow \ \color{red}{6x \ - \ 18= 36 \times 7}$

$\ \Rightarrow \ \color{red}{x = \frac{ 252 \ + \ 18}{6} = 45}$

$\frac{ 4x \ - \ 20}{6} = 52$

$\ \Rightarrow \ \color{red}{4x \ - \ 20= 52 \times 6}$

$\ \Rightarrow \ \color{red}{x = \frac{ 312 \ + \ 20}{4} = 83}$

$3x \ - \ 15 = -6$

$\ \Rightarrow \ \color{red}{x = \frac{-6 \ + \ 15}{3} = 3}$

$2(x \ - \ 10) = 38$

$\ \Rightarrow \ \color{red}{x \ - \ 10= \frac{38}{2}}$

$\ \Rightarrow \ \color{red}{ x = 19 \ + \ 10 = 29}$

$2x \ - \ 6 = -2$

$\ \Rightarrow \ \color{red}{x = \frac{-2 \ + \ 6}{2} = 2}$

$\frac{ 2x \ - \ 6}{5} = 14$

$\ \Rightarrow \ \color{red}{2x \ - \ 6= 14 \times 5}$

$\ \Rightarrow \ \color{red}{x = \frac{ 70 \ + \ 6}{2} = 38}$

$\frac{ 3x \ - \ 12}{4} = 42$

$\ \Rightarrow \ \color{red}{3x \ - \ 12= 42 \times 4}$

$\ \Rightarrow \ \color{red}{x = \frac{ 168 \ + \ 12}{3} = 60}$

10)

$6(x \ - \ 12) = 72$

$\ \Rightarrow \ \color{red}{x \ - \ 12= \frac{72}{6}}$

$\ \Rightarrow \ \color{red}{ x = 12 \ + \ 12 = 24}$

How to Solve Two Step Equations