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Sec. 6.3
Solving Multi-Step Inequalities
Solving Multi-Step Inequalities
There are some inequalities that involve more than one operation. It can be solved by undoing the
operations in the same way you would solve a multi-step equation.
Ex.1 Inequality Involving a Negative Coefficient
Solve -7b + 19 < -16
Your Turn
23 > 10 - 2w
Ex. 2 Write and Solve an Inequality
Define a variable, write an inequality and solve the problem.
Three times a number minus eighteen is at least five times the number plus twenty one.
Your Turn
Two more than half of a number is greater than twenty-seven
When solving equations that contain grouping symbols, first use the Distributive Property to remove the
grouping symbols.
Ex. 3 Distributive Property
a.
-3(2 + 3b) ≤ 2
b. 3d - 2(8d - 9) > -2d - 4
Your Turn
6(5z - 3) ≤ 36z
If solving an inequality results in a statement that is always true, the solution set is the set of all real
numbers. This is written as
{x l x is a real number}
If solving an inequality results in a statement that is never true, the solution set is an empty set, written as
the symbol O. The empty set has no members.
Ex. 4 Empty Set and All Reals
Solve each inequality
a.
8(t + 2) - 3(t - 4) < 5(t - 7) + 8
b. 3(p +4) - p +12 ≤ 2(p + 12)
Your Turn
18 - 3(8c + 4) ≥ -6(4c - 1)