Solving two step inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

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

Back

First, subtract 14 from both sides to get -4x ≤ 40. Then, divide both sides by -4, remembering to reverse the inequality sign, resulting in x ≥ -10.

Front

What does it mean to reverse the inequality sign when dividing by a negative number?

Back

When you divide or multiply both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

Front

What is the solution to the equation 3x + 7 = -8?

Back

To solve for x, subtract 7 from both sides to get 3x = -15, then divide by 3 to find x = -5.

Front

How do you isolate the variable in the inequality x < -20?

Back

To isolate x, you simply interpret the inequality as stating that x is any number less than -20.

Front

What is the first step in solving the equation -5t + 9 = 24?

Back

The first step is to subtract 9 from both sides, resulting in -5t = 15.

Front

What is the final solution for t in the equation -5t + 9 = 24?

Back

After isolating t, divide both sides by -5 to get t = -3.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

Front

What does the solution x < -20 represent on a number line?

Back

It represents all the numbers to the left of -20 on the number line, indicating that x can take any value less than -20.

Front

How do you check the solution of an inequality?

Back

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