Solving Multi-Step Inequalities with Word Problems

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division.

Front

How do you solve the inequality 3(x - 2) < 2(x + 9)?

Back

First, distribute: 3x - 6 < 2x + 18. Then, subtract 2x from both sides: x - 6 < 18. Finally, add 6 to both sides: x < 24.

Front

What does the inequality 6 > x mean?

Back

It means that x is less than 6.

Front

If Eleni bought 2 pounds of grapes at $3.49 per pound, how do you calculate her total cost?

Back

Multiply the price per pound by the number of pounds: 2 * 3.49 = $6.98.

Front

How do you find the change Eleni received after paying with a $10 bill?

Back

Subtract the total cost from the amount paid: $10 - $6.98 = $3.02.

Front

What inequality represents the amount each choir member needs to raise to meet a goal of $1,500 after raising $600?

Back

30x + 600 ≥ 1,500, where x is the amount each member raises.

Front

How do you solve the inequality -2x + 3(-4x + 6) ≤ 116?

Back

First, distribute: -2x - 12x + 18 ≤ 116. Combine like terms: -14x + 18 ≤ 116. Then, subtract 18: -14x ≤ 98. Finally, divide by -14 (remember to flip the inequality): x ≥ -7.

Front

What is the solution set for the inequality x < 24?

Back

The solution set includes all real numbers less than 24.

Front

What does the symbol '≥' mean in an inequality?

Back

It means 'greater than or equal to'.

Front

What is the first step in solving a multi-step inequality?

Back

Identify and isolate the variable by performing inverse operations.