Question

1. write the property that justifies each step. solve $4x - 10 = 5x + 17$.

$4x - 10 = 5x + 17$
$-1x - 10 = 17$
$-1x = 27$
$x = -27$

1. write the property that justifies each step. solve $\frac{5x}{6} + 1 = 6$.

$\frac{5x}{6} + 1 = 6$
$5x + 6 = 36$
$5x = 30$
$x = 6$

1. consider the statement “if a triangle has three equal sides, then it is an equilateral triangle.”

the hypothesis is
the conclusion is

1. let $p$ be “a shape is a triangle” and let $q$ be “the shape has three angles.” combine these to write the following versions.

condition statement:
converse:
inverse:
contrapositive:

Explanation:

Problem 6

Step1: Original equation

$4x - 10 = 5x + 17$

Step2: Subtract $4x$ (Subtraction Prop. of Eq.)

$-1x - 10 = 17$

Step3: Add 10 (Addition Prop. of Eq.)

$-1x = 27$

Step4: Divide by -1 (Division Prop. of Eq.)

$x = -27$

Step1: Original equation

$\frac{5x}{6} + 1 = 6$

Step2: Multiply by 6 (Multiplication Prop. of Eq.)

$5x + 6 = 36$

Step3: Subtract 6 (Subtraction Prop. of Eq.)

$5x = 30$

Step4: Divide by 5 (Division Prop. of Eq.)

$x = 6$

In a conditional statement "If P, then Q", P is the hypothesis (the condition) and Q is the conclusion (the result of the condition).

Answer:

Justifications (in order): Given equation, Subtraction Property of Equality, Addition Property of Equality, Division Property of Equality; $x=-27$

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Problem 7