Solving Equations and Inequalities

Front

What is the first step to solve the equation 46 + 7x = 95?

Back

Subtract 46 from both sides of the equation.

Front

How do you isolate the variable 'a' in the equation 19 + a = -50?

Back

Subtract 19 from both sides to get a = -69.

Front

What does the inequality 5x - 4 > 21 represent on a number line?

Back

It represents all values of x greater than 5.

Front

Identify the mistake in the equation 19 - 2k = 3k - 1 when trying to isolate k.

Back

The mistake is adding 3k instead of subtracting 3k.

Front

What is the solution to the inequality -7x - 13 ≥ 8?

Back

x ≤ -3.

Front

What is the general form of a linear equation?

Back

The general form is Ax + By = C, where A, B, and C are constants.

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

How do you graph the solution of an inequality on a number line?

Back

Use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate direction.

Front

What is the purpose of checking your solution in an equation?

Back

To verify that the solution satisfies the original equation.

Front

What does it mean to 'isolate the variable' in an equation?

Back

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