Solving Two-Step Inequalities

Front

What does the symbol '≥' represent in inequalities?

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you solve the inequality 2x + 6 ≥ -8?

Back

To solve the inequality, subtract 6 from both sides to get 2x ≥ -14, then divide by 2 to find x ≥ -7.

Front

What is the solution to the inequality y + 7 ≥ 12?

Back

The solution is y ≥ 5, found by subtracting 7 from both sides.

Front

What does the inequality b ≤ -2 indicate about the value of b?

Back

The inequality b ≤ -2 indicates that b can be any value less than or equal to -2.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

To solve, subtract 14 from both sides to get -4x ≤ 40, then divide by -4 (remember to flip the inequality) to find x ≥ -10.

Front

What is the difference between '>' and '≥'?

Back

The symbol '>' means 'greater than' while '≥' means 'greater than or equal to', including the boundary value.

Front

How can you graph the inequality x ≥ -7 on a number line?

Back

To graph x ≥ -7, draw a solid dot on -7 and shade to the right to indicate all values greater than -7.

Front

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

Back

The first step is to isolate the variable term by performing inverse operations, similar to solving an equation.

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution if the variable cannot satisfy the inequality, such as x > x.

Front

How do you check your solution for an inequality?

Back

To check your solution, substitute the value back into the original inequality to see if it holds true.