Mathematics from zero
Algebra: multiple-choice review
Six questions that cut across the whole unit. Each one is a small piece of work — substitute, simplify, or solve — not a definition to recite. Do the arithmetic, then pick the choice that matches and read why the others miss.
Confirm you can connect the unit’s four ideas — a variable as a stand-in number, an expression as a recipe for a value, an equation as a balance you solve, and an inequality as a range — and apply them to fresh problems.
The variable n stands for 6. What is the value of the expression 2n + 5?
Simplify the expression 3x + 4 + 5x as far as it will go.
To solve 2x + 1 = 9, you first subtract 1. Where must that subtraction happen, and why?
Solve 3x + 2 = 20 for x.
You solve an inequality and reach x > 4. What is the full solution?
Which statement is an equation rather than a bare expression, and what makes the difference?
The through-line of the unit is one chain. A variable names a number you may not know yet; an expression strings variables, numbers, and operations into a recipe you evaluate by substituting and simplify by combining like terms; an equation adds an equals sign and a claim, which you solve by doing the same move to both sides until the variable stands alone; an inequality swaps the equals sign for a comparison, so its answer is a whole range. Same balance rule throughout — the question just gets looser as you go.