Solve for \( x \) in the linear equation \( 3x + 7 = 22 \) - Math Solver AI

$Math Problem$

Mathematics Grade 7

Question Content

Solve for \( x \): \( 3x + 7 = 22 \)

Correct Answer

\( x = 5 \)

Detailed Solution Steps

1
Step 1: Subtract 7 from both sides of the equation to isolate the term with \( x \). \n\( 3x + 7 - 7 = 22 - 7 \)
2
Step 2: Simplify both sides. \n\( 3x = 15 \)
3
Step 3: Divide both sides by 3 to solve for \( x \). \n\( \frac{3x}{3} = \frac{15}{3} \)
4
Step 4: Simplify. \n\( x = 5 \)

Knowledge Points Involved

1

Linear Equation in One Variable

A linear equation in one variable is an equation of the form \( ax + b = c \), where \( a \), \( b \), and \( c \) are constants, and \( a \neq 0 \). It represents a straight line when graphed (in two dimensions) and has exactly one solution for \( x \) when solved.

2

Properties of Equality

The properties of equality state that if we add, subtract, multiply, or divide both sides of an equation by the same non - zero number, the equation remains true. For example, if \( a = b \), then \( a + c = b + c \), \( a - c = b - c \), \( a\times c = b\times c \) (for \( c\neq0 \)), and \( \frac{a}{c}=\frac{b}{c} \) (for \( c\neq0 \)).

3

Algebraic Manipulation

Algebraic manipulation involves performing operations (such as addition, subtraction, multiplication, division, and combining like terms) on algebraic expressions to simplify them or solve equations. In this problem, we combined the constant terms (by subtracting 7) and then isolated the variable \( x \) (by dividing by 3).

Loading solution...