Chapter 1; Linear Equations: Sections 1.4 - 1.5 (VIVI)

If you see an absolute value on one side of an equation and a negative value on the other, is there automatically no solution?

No; If there are additional terms on the absolute value's side of the equation, it may simplify to an eqution that can be solved. Ex: -2 | 4x - 7 | = -12 Divide both sides by -2 + | 4x - 7 | = 6

When showing your work to solve an equation, you must always justify which __________ you used.

Properties of Equality

Ex) What properties would you use to solve 7x = 3y + x for y? What is the solution?

Subtraction Property of Equality: Subtract x from both sides to separate the variables. Division Property of Equality: Divide both sides by 3 to isolate the variable, y. The solution is y = 2x.

How many solutions are in an absolute value equations y to x?

Three; Infinitely many solutions, One solution, No solution

If there are values outside of the absolute value symbols in an equation, what must you do to isolate the absolute value?

Use inverse operations to isolate the absolute value.

Ex) When asked to solve | x - 5 | = 8, what is the first step?

Write the equations x - 5 = 8 and x - 5 = -8.

Is it important to check the answer(s) you got for absolute value equations? Why or why not?

Yes; Solution might be extraneous and doesn't satisfy original equation.

How do you figure out if a solution is an extraneous solution?

You substitute the solution into the original equation. If both sides of the equation are not equal, it is an extraneous solution.

When solving an absolute value equation, what two linear equations do you write? (Ex: | a - b | = c )

1.) a - b = c ; no absolute value symbols 2.) a - b = -c ; no absolute value symbols and c is a negative

Ex) Which property would be used to solve x - 8 = 4y for x? What is the solution?

Addition Property of Equality: Add 8 to both sides to isolate the variable, y. The solution is x = 4y + 8.

If the absolute values of two algebraic expressions are equal, then they must be either __________ or __________.

Equal to each other; Opposite to each other

True or False: An absolute value equation can equal a negative number.

False

When writing an absolute value equation that includes a minimum and a maximum, what format should you follow if the out come id false?

| x - halfway point | = distance from the halfway point