Solving Equations and Inequalities

Front

What is the first step in solving the inequality 5(6 + 3r) + 7 ≥ 127?

Back

Distribute the 5 to both terms inside the parentheses: 30 + 15r + 7 ≥ 127.

Front

How do you isolate the variable in the equation 4x + 2(x - 6) = 12?

Back

Combine like terms: 4x + 2x - 12 = 12, then add 12 to both sides and combine terms.

Front

What does it mean when an equation has infinitely many solutions?

Back

It means that the equation is true for all values of the variable, often resulting from equivalent expressions.

Front

What is the solution to the inequality -4x + 14 ≤ 54?

Back

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

Front

What is the process to solve the equation 5x + 34 = -2(-7x + 1)?

Back

Distribute -2 to get 5x + 34 = 14x - 2, then isolate x by moving terms involving x to one side.

Front

What is the significance of the term 'inequality' in mathematics?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is less than, greater than, or not equal to the other.

Front

How do you check if your solution to an equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.

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 'isolate the variable' in an equation?

Back

To isolate the variable means to manipulate the equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the solution to the equation 3x + 15 = 3(x + 5)?

Back

This simplifies to 3x + 15 = 3x + 15, which is true for all x, indicating infinitely many solutions.