Solving 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

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 3(2e + 5) + 8(1 - e) = 1?

Back

First, distribute: 6e + 15 + 8 - 8e = 1. Combine like terms: -2e + 23 = 1. Subtract 23 from both sides: -2e = -22. Divide by -2: e = 11.

Front

What does it mean to solve an inequality?

Back

Solving an inequality involves finding the values of the variable that make the inequality true. The solution is often expressed in interval notation or on a number line.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40. Divide by -4: x ≥ -10.

Front

What is the solution to the inequality -3 - 6(4x + 6) > -111?

Back

Distribute: -3 - 24x - 36 > -111. Combine like terms: -24x - 39 > -111. Add 39: -24x > -72. Divide by -24: x < 3.

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, less than, or not equal to another.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means rearranging an equation or inequality so that the variable is on one side and all other terms are on the opposite side.

Front

How do you check your solution for an equation?

Back

To check your solution, substitute the value back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 0.75 + 2(a - 0.5) = 3a - 0.4?

Back

Distribute: 0.75 + 2a - 1 = 3a - 0.4. Combine like terms: -0.25 + 2a = 3a - 0.4. Rearranging gives: 0.15 = a.