Solving Equations and Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

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

Back

1. Subtract 14 from both sides: -4x ≤ 40. 2. Divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What is the first step in solving the equation 19 - 2k = 3k - 1?

Back

The first step is to isolate the variable k by moving all terms involving k to one side. You should subtract 3k from both sides.

Front

What is the error in the equation 19 - 2k = 3k - 1?

Back

Instead of adding 3k, they should subtract 3k.

Front

How do you solve the inequality -3 - 6(4x + 6) > -111?

Back

1. Distribute: -3 - 24x - 36 > -111. 2. Combine like terms: -24x - 39 > -111. 3. Add 39 to both sides: -24x > -72. 4. Divide by -24 (flip the inequality): x < 3.

Front

What does it mean to isolate a variable in an equation?

Back

Isolating a variable means to manipulate the equation so that the variable is on one side by itself, making it easier to solve.

Front

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

Back

1. Distribute: 30 + 15r + 7 ≥ 127. 2. Combine like terms: 15r + 37 ≥ 127. 3. Subtract 37: 15r ≥ 90. 4. Divide by 15: r ≥ 6.

Front

What is the solution to the equation 4x + 2(x - 6) = 12?

Back

1. Distribute: 4x + 2x - 12 = 12. 2. Combine like terms: 6x - 12 = 12. 3. Add 12: 6x = 24. 4. Divide by 6: x = 4.

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 or less than another.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.