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:

6.

Step1: Subtract 4x from both sides

Starting with $4x - 10=5x + 17$, subtracting $4x$ from both sides gives $4x-4x - 10=5x-4x + 17$, which simplifies to $-1x - 10 = 17$. The property used is the Subtraction Property of Equality.

Step2: Add 10 to both sides

Given $-1x - 10 = 17$, adding 10 to both sides: $-1x-10 + 10=17 + 10$, resulting in $-1x=27$. The property used is the Addition Property of Equality.

Step3: Divide both sides by - 1

Since $-1x = 27$, dividing both sides by -1: $\frac{-1x}{-1}=\frac{27}{-1}$, so $x=-27$. The property used is the Division Property of Equality.

Step1: Multiply both sides by 6

Starting with $\frac{5x}{6}+1 = 6$, multiplying each term by 6 using the Multiplication Property of Equality: $6\times\frac{5x}{6}+6\times1=6\times6$, which simplifies to $5x + 6=36$.

Step2: Subtract 6 from both sides

Given $5x + 6=36$, subtracting 6 from both sides: $5x+6 - 6=36 - 6$, resulting in $5x = 30$. The property used is the Subtraction Property of Equality.

Step3: Divide both sides by 5

Since $5x = 30$, dividing both sides by 5: $\frac{5x}{5}=\frac{30}{5}$, so $x = 6$. The property used is the Division Property of Equality.

In a conditional statement of the form "If p, then q", p is the hypothesis and q is the conclusion. For the statement "If a triangle has three equal sides, then it is an equilateral triangle", the hypothesis is the part that follows "If" and the conclusion is the part that follows "then".

Answer:

The properties are: Subtraction Property of Equality, Addition Property of Equality, Division Property of Equality

7.