Linear Inequalities

Absolute value inequalities describe distances. Inequalities of the form $|x-a|<b$ describe values within $b$ units of $a$, while $|x-a|>b$ describes values more than $b$ units away.

Compound inequalities require the same operation on each part. Endpoint type matters when counting integers.

Context problems often translate into equations or inequalities by tracking units. Totals, budgets, minimums, and maximums determine the operation and inequality direction.

Words such as at most, at least, minimum, maximum, and budget indicate inequality direction. Integer contexts may require rounding up or down.

Inequality questions are error-prone because strict versus inclusive endpoints, negative division, compound inequalities, and integer boundaries all affect the final answer.

When solving inequalities, multiplying or dividing by a negative number reverses the inequality sign. This is a common source of wrong answers.

Linear inequalities use symbols such as $<$, $>$, $\le$, and $\ge$ to describe ranges of values. Solving them is similar to solving linear equations, except the inequality symbol reverses when both sides are multiplied or divided by a negative number.

Linear inequalities use symbols such as $<$, $>$, $\le$, and $\ge$ to describe ranges of values. Solving them is similar to solving linear equations, except the inequality symbol reverses when both sides are multiplied or divided by a negative number.

Linear inequalities use symbols such as $<$, $>$, $\le$, and $\ge$ to describe ranges of values. Solving them is similar to solving linear equations, except the inequality symbol reverses when both sides are multiplied or divided by a negative number.

Linear inequalities use symbols such as $<$, $>$, $\le$, and $\ge$ to describe ranges of values. Solving them is similar to solving linear equations, except the inequality symbol reverses when both sides are multiplied or divided by a negative number.

Parameter questions for inequalities often require identifying the coefficient that produces a stated solution set.

Linear inequalities use symbols such as $<$, $>$, $\le$, and $\ge$ to describe ranges of values. Supplemental practice should emphasize integer boundary questions, compound inequalities, strict versus inclusive endpoints, context constraints, and parameter values that determine a solution set.

Inequality questions use symbols to represent limits, minimums, maximums, and ranges. Contexts often require translating phrases such as at least, at most, fewer than, or no more than.