# Equations and Inequalities-Target A-Prove It-Guided Learning

Equations and Inequalities-Target A: Use Algebraic Proofs to justify the steps to solve a linear equation or inequality including one solution, no solution or infinitely many solutions.

 $\dfrac{1}{2}x+8 = \text{-}7$ Jessica claims that the first step to solve the above equation is to add negative 8 to both sides of the equation. Kathleen claims that the first step to solve the equation is to multiply each side of the equation by 2. Whom do you agree with and why?

To review how to solve an equation, click on the link below:
Multi-step Equation, Clearing Fractions, Variables on Both Sides, and Equations with Special Solutions (No Solution vs. Infinitely Many Solutions)

Algebraic Proofs
An algebraic proof is a series of logical statements that are used to reach a conclusion. Basically, it means that as you solve an equation, you provide a reason for each step. Some of the reasons that can be used in an algebraic proof are as follows:

A common format used for algebraic proofs is two column. One column is labeled STATEMENTS, and the other column is labeled REASONS. The "STATEMENTS" column is where you write each equivalent equation as you solve, and the "REASONS" column is where you write the justification (choose the correct property from the list above) for each step.

When creating a proof, use the "given" statement as the first statement in the proof, and continue writing equivalent equations until you have reached the "prove" statement. When filling out the two columns, make sure not to show the work within the proof. So, you may need to solve the equation first, before setting up your algebraic proof. Look at the example below.

Equations and Inequalities-Target A-Prove It-Quick Check

Fill in the statements for the following algebraic proof.

Equations and Inequalities-Target A-Prove It-Quick Check Solutions