Q.A plumber can be paid according to the following schemes: In the first scheme he will be paid rupees 500 plus rupees 70 per hour, and in the second scheme he will paid rupees 120 per hour. If he works $x$ hours, then for what value of $x$ does the first scheme give better wages?

A linear inequality is solved exactly like a linear equation, with ONE crucial exception: multiplying or dividing both sides by a negative number reverses the inequality's direction; multiplying by a positive number never does.

Systems ('and'/'or'). Combining two inequalities with 'and' takes the intersection of their solution sets; combining with 'or' takes the union -- and when one solution ray is already a subset of the other, the union collapses to just the larger one (e.g. '$x<-1$ or $x<3$' is simply $x<3$).

Clearing fractions. Multiply both sides by the LCM of all denominators (a positive number, so no flip) before isolating the variable. …