Much like solving equations from real world problems, there are certain keywords or phrases to look out for. When it comes to inequalities, we now have a few extra keywords and phrases to represent the different inequality symbols.

Keywords:

\gt

**greater than**, more than.\geq

**greater than or equal to**, at least, no less than.\lt

**less than**.\leq

**less than or equal**to, at most, no more than.

When working to solve problems always be sure to check your answer to see if it is reasonable and then check it by substituting into your inequality.

Consider the following situation:

"The sum of 2 groups of x and 1 is at least 7."

a

Construct and solve an inequality for the given situation.

Worked Solution

b

Does the solution x=-3 satisfy the inequality?

Worked Solution

Lachlan is planning on going on vacation. He has saved \$2118.40, and spends \$488.30 on his airplane ticket.

a

Let x represent the amount of money Lachlan spends on the rest of his holiday. Write an inequality to represent the situation, and then solve for x.

Worked Solution

b

What is the most that Lachlan could spend on the rest of his holiday?

Worked Solution

At a sport clubhouse the coach wants to rope off a rectangular area that is adjacent to the building. He uses the length of the building as one side of the area, which measures 26 meters. He has at most 42 meters of rope available to use.

If the width of the roped area is W, form an inequality and solve for the range of possible widths.

Worked Solution

The student government association is planning a seventh grade dance as a fundraiser. It costs \$250 to pay for the DJ and decorations. Tickets to the dance cost \$8 each. How many tickets must they sell to raise at least \$1000?

Worked Solution

Consider the following inequality: 3.7+ 8 x \geq 19.5

a

Create a real world scenario that could be represented by the equation.

Worked Solution

b

Solve the inequality and explain the answer in context to the scenario you created.

Worked Solution

Idea summary

Keywords and phrases to represent the different inequality symbols:

\gt greater than, more than.

\geq greater than or equal to, at least, no less than.

\lt less than.

\leq less than or equal to, at most, no more than.