Algebra 1 Review

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, or not equal to the other.

Front

How do you solve the inequality 8 - 4x < 20?

Back

Subtract 8 from both sides: -4x < 12. Then divide by -4 (remember to flip the inequality): x > -3.

Front

What does the solution x > -3 represent on a number line?

Back

It represents all numbers to the right of -3, not including -3 itself.

Front

What is the solution for the inequality 14 < -2a + 6 - 2a?

Back

Combine like terms: 14 < -4a + 6. Then subtract 6 from both sides: 8 < -4a. Divide by -4 (flip the inequality): a < -2.

Front

How do you solve the equation 32 - x = -3(x - 4)?

Back

Distribute -3: 32 - x = -3x + 12. Add x to both sides: 32 = -2x + 12. Subtract 12: 20 = -2x. Divide by -2: x = -10.

Front

What is the solution for the equation x = 10?

Back

This means that the value of x is 10.

Front

How do you simplify the expression (5x + 20) ÷ 5?

Back

Divide each term by 5: (5x ÷ 5) + (20 ÷ 5) = 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 'solve for x'?

Back

To solve for x means to find the value of x that makes the equation or inequality true.

Front

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

Back

Flipping the inequality sign ensures that the relationship between the two sides of the inequality remains true.