Practice linear equations with unique questions about one-step equations, two-step equations, equations with parentheses, variables on both sides, and real-life algebra problems. Use hints when needed, choose an answer, and review the explanation after each question.
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The 10 questions move from direct one-step equations to equations with constants, division, parentheses, a negative coefficient, variables on both sides, and a short word problem. The central skill is the same throughout: transform both sides without changing the set of solutions.
Undo addition, subtraction, multiplication, or division in a controlled order to isolate x.
Collect variable terms on one side and constants on the other before dividing by the final coefficient.
Decide whether distributing first or undoing an outside factor first creates the shorter solution path.
Translate a relationship described in words into an equation before carrying out the algebra.
Consider 4(2x − 3) − 5 = 3x + 18. Each line must produce an equation equivalent to the one before it.
Linear equations do not need one rigid procedure. A useful first move is the one that simplifies the structure while keeping both sides equivalent.
Dividing both sides by 2 immediately gives x + 3 = 9. Distribution also works, but it creates an extra step.
Move variable terms together first: subtract 2x from both sides, then remove the constant and divide.
Here distribution exposes the x-terms clearly: 4x − 8 = 2x + 10, after which like terms can be collected.
The coefficient of x is −1. Keeping that sign visible prevents the common error of reporting x = −5 instead of x = 5.
Suppose Plan A charges a fixed $24 fee plus $6 per gigabyte, while Plan B charges a fixed $42 fee plus $3 per gigabyte. Let g be the number of gigabytes used.
Plan A: fixed cost + 6 dollars for each gigabyte.
Plan B: larger fixed cost + 3 dollars for each gigabyte.
To find when the plans cost the same, set their total costs equal.
At 6 GB, both plans cost $60. The equation does more than find a number: it identifies the point where two linear cost models intersect.
An equation remains equivalent only when the same valid operation is applied to both sides.
In equations such as 7 − x = 2, the variable term is −x. Its sign must be preserved until the final step.
A factor outside parentheses multiplies every term inside the parentheses.
Review inverse operations and one- or two-step equations before focusing on parentheses or variables on both sides.
The foundation is forming. Review the exact equation types you missed and solve one new example of each without a hint.
You are ready for more equations with variables on both sides, parentheses, inequalities, and multi-step modeling.