Algebra 1 is one idea applied repeatedly: whatever you do to one side of an equation, do to the other. Everything else. Lines, systems, inequalities, is that idea plus notation.
Practise algebraIsolating a variable means undoing operations in reverse order. Clear brackets, collect like terms on one side, then undo addition before multiplication, mirroring the order of operations backwards.
Equations with fractions are easier if you multiply through by the least common denominator first. This produces an equivalent equation with integer coefficients, which cuts arithmetic slips dramatically.
Inequalities follow the same moves as equations with one exception: multiplying or dividing by a negative number reverses the direction of the sign. Forgetting that single rule accounts for most lost marks in this topic.
Solutions are intervals rather than points, so express them consistently. Either in interval notation or on a number line, and be explicit about whether endpoints are included.
Slope is a rate of change: rise over run. A positive slope climbs left to right, a negative slope falls, zero is horizontal, and undefined slope is vertical because the run is zero.
Choose the form that matches what you know. Slope-intercept is best when you have the y-intercept, point-slope when you have any point and the slope, and standard form when you need integer coefficients.
Two lines can meet once, never, or everywhere, which corresponds to one solution, no solution, or infinitely many. Recognising the parallel and identical cases early saves pointless algebra.
Substitution suits systems where a variable is already isolated; elimination suits systems where coefficients line up or can be scaled to cancel. Graphing is a check, not a solution method, because intersections are rarely exact.
