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

$Math Problem$

Mathematics Grade 7 (Junior High School)

Question Content

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

Correct Answer

\( x = 5 \)

Detailed Solution Steps

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

Knowledge Points Involved

1

Linear Equations in One Variable

An equation of the form \( ax + b = c \) (where \( a \neq 0 \)) that involves only one variable (\( x \)) with a highest power of 1. Solving it requires isolating the variable using inverse operations.

2

Inverse Operations

Operations that reverse the effect of another operation (e.g., subtraction reverses addition, division reverses multiplication). Used here to isolate \( x \) by undoing addition (subtract 7) and multiplication (divide by 3).

3

Equation Balance Principle

To keep an equation true, any operation (e.g., adding, subtracting, multiplying, dividing) must be applied to both sides of the equation. This ensures the equality remains valid.

Loading solution...