Solving Equations and Algebraic Properties Worksheet

Front

What does the equation 2x + 8 = 3 + 2x represent?

Back

This equation has no solution because both sides simplify to the same expression, indicating a contradiction.

Front

What is the Distributive Property in algebra?

Back

The Distributive Property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside parentheses.

Front

How do you combine like terms in the expression 2x + 18 = 4x + 28?

Back

You can combine like terms by moving all terms involving x to one side and constant terms to the other.

Front

What is the Subtraction Property of Equality?

Back

The Subtraction Property of Equality states that if you subtract the same number from both sides of an equation, the two sides remain equal.

Front

What does the symbol 'x ≥' mean?

Back

The symbol 'x ≥' means that x is greater than or equal to a certain value.

Front

How many solutions does the equation 7x + 10 = 7x + 10 have?

Back

This equation has infinitely many solutions because both sides are identical.

Front

What is the first step to solve the equation (3/4)(x + 8) = 9?

Back

Multiply both sides by the reciprocal of 3/4, which is 4/3, to eliminate the fraction.

Front

What is the value of x in the equation 2(x + 9) = 4(x + 7)?

Back

x = -6 after applying the Distributive Property and solving for x.

Front

What does it mean if an equation has no solution?

Back

It means that there is no value for the variable that can satisfy the equation.

Front

What is the purpose of the Division Property of Equality?

Back

The Division Property of Equality states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal.