The first step is to convert the following into a mathematical equation:

There are 10 sugar cubes on a small tray. Jim takes 1 cube for his tea, and Jack takes twice as many cubes as Jim.

The equation for the remaining cubes would be:

\(\displaystyle 10-1-2*1=7\)

Therefore, 7 is the correct answer. 

If Anita adopted more cats than Bob, then she adopted more than 2 cats. 

Given that Bob adopted 2 cats, there are 7 cats remaining. A majority of the remaining cats would be 4. 

Given that Anita adopted more than 2 cats, but less than 4, she must have adopted 3 cats; therefore, 3 is the correct answer. 

If Tom has 8 pretzel sticks and gives one stick to his sister, then he will have 7 pretzel sticks remaining. If he then breaks what remains in half, he will have 14 half-pretzel sticks. If Tom eats 5 of the half-pretzel sticks, 9 half-pretzel sticks will therefore remain. 

Subtract the numbers and keep the variable:

\(\displaystyle 14s-3s=11s\)

Answer: \(\displaystyle 11s\)

First distribute the subtraction sign through the terms in the parentheses. 

\(\displaystyle -(3x) = -3x\)

Subtraction of a negative is the same as adding a positive.

\(\displaystyle - (12xy) = 12xy\)

Rewrite.

\(\displaystyle 18x + 43xy - 5x -3x +12xy\)

Group all like terms together.

\(\displaystyle (18x -5x - 3x) + (42xy + 12xy)\)

Evaluate the terms in each parentheses.

\(\displaystyle (18x-5x-3x) = 10x\)

\(\displaystyle (42xy + 12xy) = 54xy\)

Rewrite in simplest form.

\(\displaystyle 10x + 54xy\) is the correct answer.

First distribute the \(\displaystyle -3\) to the terms inside the parentheses.  

\(\displaystyle -3 (5x) = -15x\)

\(\displaystyle -3 (-5y) = 15y\)

\(\displaystyle -3 (2) = -6\)

Rewrite.

\(\displaystyle 22x -20y -15x + 15y -6\)

Rewrite putting like terms together.

\(\displaystyle (22x-15x) + (-20y +15y) -6\)

Evaluate each set of terms in the parentheses.

\(\displaystyle (22x-15x) = 7x\)

\(\displaystyle (-20y + 15y) = -5y\)

The constant is \(\displaystyle -6.\)

Rewrite in simplest form.

\(\displaystyle 7x -5y -6\) is the correct answer.

The first step in simplifying the expression

\(\displaystyle 6x^{2} +2x^{2}y -3y - 4(3x^{2}y -2x^{2 }+2)\) is to distribute the \(\displaystyle -4\) to all terms inside the parentheses.

\(\displaystyle -4 (3x^{2}y) = -12x^{2}y\)

\(\displaystyle -4 (-2x^{2}) = 8x^{2}\)

\(\displaystyle -4 (2) = -8\)

Rewrite.

\(\displaystyle 6x^{2} +2x^{2}y-3y -12x^{2}y + 8x^{2} -8\)

Group like terms together. Rewrite.

\(\displaystyle (6x^{2} + 8x^{2}) + (2x^{2}y-12x^{2}y) -3y-8\)

Evaluate the terms in the parentheses.

\(\displaystyle (6x^{2} + 8x^{2}) = 14x^{2}\)

\(\displaystyle (2x^{2}y - 12x^{2}y) = -10x^{2}y\)

There are no terms to combine with\(\displaystyle -3y\) and the constant which is \(\displaystyle -8\)

Rewrite in simplest form.

\(\displaystyle 14x^{2} -10x^{2}y -3y -8\) is the correct answer.

Distribute the 4 to all terms in the parentheses.

\(\displaystyle 4 (x+7) = 4x +28\)

Rewrite.

\(\displaystyle 12x - 4x- 28\)

Combine like terms.

\(\displaystyle 12x-4x =8x\)

Rewrite in simplest form.

\(\displaystyle 8x-28\) is the correct answer.

\(\displaystyle 30 - 5 (x + 4)\)

When solving this problem we need to remember our order of operations, or PEMDAS. 

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable  to a number, so we move to the next step. 

Multiplication: We can distribute (or multiply) the \(\displaystyle -5\). 

\(\displaystyle = 30 - 5 \cdot x + (- 5) \cdot 4\)

\(\displaystyle = 30 - 5 x + (- 20)\)

Addition/Subtraction: Remember, we can't add a variable  to a number, so the \(\displaystyle -5x\) is left alone.

\(\displaystyle = - 5 x + 30 - 20\)

\(\displaystyle = -5x + 10\)

When solving this problem we need to remember our order of operations, or PEMDAS. 

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable  to a number, so we move on to the next step

Multiplication: We can distribute the negative sign to the \(\displaystyle 4x\) and \(\displaystyle -7\)

\(\displaystyle (3x+2)-(4x-7)\)

\(\displaystyle =3x+2-4x-(-7)\)

Remember, a negative times a negative will equal a positive, so we have a \(\displaystyle +7\)

\(\displaystyle =3x+2-4x+7\)

Finally we can combine like terms

\(\displaystyle 3x-4x=-x\)

\(\displaystyle 2+7=9\)

\(\displaystyle =-x+9\)