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Inequalities

# Solve two-step linear inequalities

A statement involving a variable and a sign of inequality (viz. < , ≤ , > or ≥) is called an inequality. A statement of inequality between two expressions consisting of a single variable, say x, of highest power 1, is called a linear inequality in one variable. It is ussually written in any of the following forms:

ax+b<0
ax+b>0
ax+b≥0
ax+b≤0

where a ≠ 0;

Linear inequalities are solved much the same way as linear equations are solved, with one important exception: when multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be reversed.

$2x-5\;<\;3\;\Rightarrow\;2x\;<\;3+5\;\Rightarrow\;2x\;<\;8\;\Rightarrow\;x\;<\;4$

$\text{Solution\;Set:}\;\{\;x\;\in\;\Re\;\text{,}\;x\;<\;4\;\}\;\text{=}\;\(-\infty,4)$

Solve for d.

40+10d ≤ -70

Solution: d