8x + 2(x − 7) = 7x + 3x − 14

part a: solve the equation and write the number of solutions. show all the steps. (6 points)

part b: name one property you used to solve this equation. (4 points)

Start with

Apply the distributive property to expand the left hand side:

Sum like terms:

Apply the additive property of equality to add 14 to both sides:

Apply the additive property of equality to subtract 10x to both sides:

This means that the equation was actually an identity, i.e. the left and right hand sides were actually the same expression.

Since they are the same expression, it doesn't matter which values you plug into x, it will always be a solution of this equation.

Solution: infinite. All numbers are solutions of this equation.

Property used: Listed while solving the equation.

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: