Multi-Step Equations and Inequalities

Front

What is a multi-step equation?

Back

A multi-step equation is an equation that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, and division.

Front

What does it mean to isolate a variable in an equation?

Back

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

Front

What is the first step in solving the equation 10(h+1)-4=76?

Back

The first step is to simplify the left side by distributing the 10: 10h + 10 - 4 = 76.

Front

How do you solve the inequality 5z - 2 - 2z < 13?

Back

Combine like terms to get 3z - 2 < 13, then add 2 to both sides to get 3z < 15, and finally divide by 3 to find z < 5.

Front

What is the solution to the inequality 14 < -2a + 6 - 2a?

Back

The solution is a < -2.

Front

What does it mean when an inequality has a 'less than' symbol (<)?

Back

It means that the value on the left side is smaller than the value on the right side.

Front

How do you check the solution of an inequality?

Back

You can check the solution by substituting a value from the solution set back into the original inequality to see if it holds true.

Front

What is the solution to the equation -7x - 36 = 20 - 3x?

Back

The solution is x = -14.

Front

What is the importance of the distributive property in solving equations?

Back

The distributive property allows you to multiply a single term by terms inside parentheses, which helps simplify equations.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values that can satisfy the inequality, often resulting in a contradiction.