Medium📚 Linear Equations
Solve Linear Equation Step by Step
Grades 7-8 (Pre-Algebra)Key Stage 3Årskurs 7-8
Problem
Solve for x: 2(x - 3) = 4x + 6
📝Step-by-Step Solution
1
Distribute on the left side
Multiply 2 by each term inside the parentheses: 2(x - 3) = 2x - 6
2x - 6 = 4x + 6
2
Get all x terms on one side
Subtract 4x from both sides to move x terms to the left: 2x - 4x - 6 = 4x - 4x + 6
-2x - 6 = 6
3
Get constants on the other side
Add 6 to both sides to isolate the x term: -2x - 6 + 6 = 6 + 6
-2x = 12
4
Solve for x
Divide both sides by -2: -2x ÷ (-2) = 12 ÷ (-2)
x = -6
5
Check the solution
Substitute x = -6: Left side: 2(-6 - 3) = 2(-9) = -18. Right side: 4(-6) + 6 = -24 + 6 = -18 ✓
✅Final Answer
x = -6
To solve linear equations: (1) Distribute to remove parentheses, (2) Combine like terms, (3) Move all variable terms to one side and constants to the other, (4) Divide to isolate the variable. Always check your answer!
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