Multi-Step Equations and Inequalities Review

Front

What is a multi-step equation?

Back

A multi-step equation is an equation that requires more than one step to solve. It often involves combining like terms, using the distributive property, and isolating the variable.

Front

How do you solve the equation 5x - 14 = 8x + 4?

Back

To solve for x, first, rearrange the equation: 5x - 8x = 4 + 14. This simplifies to -3x = 18, so x = -6.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when the two sides are never equal, such as in the case of parallel lines. For example, -5x + 13 = -5(x + 2.3) simplifies to a false statement.

Front

What is the solution to the equation 10(h+1)-4=76?

Back

To solve for h, first simplify: 10h + 10 - 4 = 76, which simplifies to 10h + 6 = 76. Then, 10h = 70, so h = 7.

Front

What is an inequality?

Back

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

Front

How do you graph the solution of an inequality?

Back

To graph an inequality, first solve for the variable, then use a number line to represent the solution set. Use an open circle for < or > and a closed circle for ≤ or ≥.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you solve the equation 5y + 34 = -2(-7y + 1)?

Back

First, distribute: 5y + 34 = 14y - 2. Then, rearrange: 5y - 14y = -2 - 34, which simplifies to -9y = -36, so y = 4.

Front

What is a solution set?

Back

A solution set is the set of all values that satisfy a given equation or inequality.

Front

What does it mean for an equation to have infinite solutions?

Back

An equation has infinite solutions when every value of the variable satisfies the equation, often resulting from equivalent expressions.