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Solving Compound Inequalities

Solving Compound Inequalities 1.5 - Solution

arrow_back Return to Solving Compound Inequalities
a
Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when you divide or multiply by a negative number, you must reverse the inequality sign.
This inequality tells us that all values less than or equal to are solutions. Note that can equal which we show with a closed circle on the number line.
b
To isolate we should subtract from both sides of the equation. Then, the fraction can be moved by multiplying by  and then dividing by
The expression tells us that all values less than or equal to will satisfy the inequality. We'll graph this with a closed circle at and the solution set marked to the left.
c
To solve the inequality, we will isolate with inverse operations.
Thus, the solution set to the inequality is all values of less than or equal to  Mark this as a closed circle on a number line and the region to the left shaded.
d
To isolate add and divide by on both sides of the inequality.
The solution set is all greater than Note that cannot equal which we show with an open circle on the number line.