# Tutor profile: Carolyn O.

## Questions

### Subject: Pre-Algebra

A rectangle has a length of 5x +9 and a width of 3x -4. The perimeter of the rectangle is 106 units. Find the length of the rectangle.

The formula for the perimeter of a rectangle is: P = 2(w + l) and P=106 Therefore, 106 = 2(5x + 9 +3x – 4) Combine like terms (9 – 4), so 106 = 2(5x + 3x +5) Combine like terms (5x + 3x) , 106 = 2(8x + 5) Distribute 2 into the parentheses 106 = 2*8x + 2*5 Therefore 106 = 16x + 10 subtract 10 from both sides 106 – 10 = 16x + 10 – 10 96 = 16x Divide by 16 on both sides 96/16 = 16x/16 6 = x Substitute 6 in for x in the length of the rectangle 5x + 9: 5(6) + 9 30 + 9 39 , therefore the length of the rectangle is 39

### Subject: Basic Math

Place these numbers in order from least to greatest: 0.075, 0.75%, 3/4

To best compare the numbers, they should be put in the same format. The percent 0.75% can be converted to a decimal by dividing 0.75 by 100, which gives 0.0075. The fraction 3/4 can be converted to a decimal by dividing 3 by 4, which gives 0.75. Placing these numbers in order from least to greatest yields 0 0075, 0.075, and 0.75 Therefore, the answer is 0.75%, 0.075, 3/4 . .

### Subject: Algebra

Create a graph that represents the solution set of: 15 – 2(x+3) < -7.

To solve and graph this inequality: 15 – 2(x+3) < -7 Distribute -2 (multiply the x and 3 in the parentheses by -2: 15 – 2x –6 < -7 Combine like terms (15 – 6) –2x + 9 < –7 Use subtraction to isolate the variable –2x +9 –9 < -7 –9 –2x < –16 Use division to solve for x –2x/–2 < –16/–2 Flip the inequality sign when multiplying or dividing by a negative x > 8 or solve this way to isolate x –2x < –16 Add 16 to both sides to set the equation equal to zero – 2x +16 < –16 +16 –2x +16 < 0 Add 2x to both sides to isolate variable – 2x +2x +16 < 0 +2x 16 < 2x divide both sides of the inequality to solve for x 16/2 < 2x/2 there fore, 8 is less than x or x is greater than 8 as above 8 < x When graphing this inequality, draw a number line with numbers less than and greater than 8. Draw an open circle on the number 8 and draw a line and arrow for the numbers greater than 8 (the arrow is pointing to the right). The circle should be open because the variable x has to be greater than 8. If inputting 8 as x, the inequality would not be true, therefore 8 can not be included as a solution.

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