Multistep inequalities

Front

What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality -p - 4p > -10?

Back

Combine like terms to get -5p > -10, then divide by -5 (remember to flip the inequality sign), resulting in p < 2.

Front

What is the first step in solving the inequality -8(x - 3) - 4x < 108?

Back

Distribute -8 to both terms inside the parentheses: -8x + 24 - 4x < 108.

Front

How do you isolate the variable in the inequality 5(6 + 3r) + 7 ≥ 127?

Back

First, distribute 5 to get 30 + 15r + 7 ≥ 127, then combine like terms to get 15r ≥ 90, and finally divide by 15 to find r ≥ 6.

Front

What does the inequality -138 ≥ -6(6b - 7) simplify to?

Back

Distributing -6 gives -138 ≥ -36b + 42. Rearranging leads to -36b ≤ -180, which simplifies to b ≥ 5 after dividing by -36.

Front

What is the solution to the inequality 6x + 2 + 6x < 14?

Back

Combine like terms to get 12x + 2 < 14, then subtract 2 to find 12x < 12, and divide by 12 to get x < 1.

Front

What is the importance of flipping the inequality sign when dividing by a negative number?

Back

Flipping the inequality sign is necessary to maintain the truth of the inequality when multiplying or dividing both sides by a negative number.

Front

What are the steps to solve a multistep inequality?

Back

1. Simplify both sides of the inequality. 2. Isolate the variable on one side. 3. Solve for the variable. 4. Check the solution.

Front

What does it mean for an inequality to be 'greater than' or 'less than'?

Back

'Greater than' means the left side is larger than the right side, while 'less than' means the left side is smaller than the right side.

Front

How can you check if your solution to an inequality is correct?

Back

Substitute the solution back into the original inequality to see if it holds true.