Caitlyn needs to solve the equation: 2(3x+1)=3(2-x). after copying the problem correctly she uses the properties of algebra to solve for x in 5 steps. there is a reason the justifies each step. what is the justification that caitlyn used for each step? name each property of algebra.
step 1 6x + 2 = 6 - 3x
step 2 2 = 6 - 9x
step 3 -4 = -9x
step 4 4/9 = x
step 5 x = 4/9

Jonathan pays $1.90 per pound for potatoes. he buys 8.3 pounds of potatoes. he determines that he will pay $15.77, before tax, for the potatoes. which best describes the reasonableness of jonathan’s solution? jonathan’s answer is reasonable because there are two decimal places in the factors and two in the product. jonathan’s answer is unreasonable because there are three decimal places in the factors and two in the product. jonathan’s answer is reasonable because is 16, and 16 is close to 15.77. jonathan’s answer is unreasonable because is 8, and 8 is not very close to 15.77.

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (-4, 0) and (6,0). the y-intercept of thefirst parabola is (0, –12). the y-intercept of the second parabola is (0-24). what is the positive difference between the avalues for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth.

Starting at home, emily traveled uphill to the hardware store for 606060 minutes at just 666 mph. she then traveled back home along the same path downhill at a speed of 121212 mph. what is her average speed for the entire trip from home to the hardware store and back?