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

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

\(\displaystyle 2+7=9\)

\(\displaystyle =-x+9\)

Divide both sides by \(\displaystyle \frac{3}{4}\):

\(\displaystyle \frac{3}{4} t = \frac{4}{3}\)

\(\displaystyle \frac{3}{4} t \div \frac{3}{4}= \frac{4}{3} \div \frac{3}{4}\)

\(\displaystyle t = \frac{4}{3} \cdot \frac{4}{3} = \frac{4\cdot 4}{3\cdot 3} = \frac{16}{9}\)

To solve: 

First, solve both equations on each end, keeping the variable.

\(\displaystyle \small 3a+ 8+ 7 = 14\cdot 3\)

\(\displaystyle 3a + 15= 42\)

Then, subtract 15 from each side of the equation.

\(\displaystyle 3a +15-15=42-15\)

\(\displaystyle 3a =27\)

Finally, divide each side by 3 so that only the variable remains.

\(\displaystyle \small 3a\div 3=27\div 3\)

\(\displaystyle \small \small a=9\)

Subtract 19, then divide by 7:

\(\displaystyle 7n + 19 = 82\)

\(\displaystyle 7n + 19-19 = 82-19\)

\(\displaystyle 7n = 63\)

\(\displaystyle 7n \div 7= 63 \div 7\)

\(\displaystyle n = 9\)

First multiply the original price by 30%.

\(\displaystyle 120\ast .30=36\)

Then subtract that amount from the original price.

\(\displaystyle 120-36=84\)

The sale price is $84.00

First solve the parentheses.

\(\displaystyle 8 * 10 \div 4=\)

Then solve from left to right since multiplication and division are interchangeable:

\(\displaystyle 80\div 4=20\)

The answer is 20.

First, convert each mixed number into an improper fraction.

\(\displaystyle \frac{20}{6}\ast \frac{11}{4}\)

Then, reduce where possible and multiply.

Finally, convert your answer into a mixed-number fraction.

\(\displaystyle \frac{55}{6}=9 {\frac{1}{6}}\)

First, convert each mixed number into an improper fraction and flip the second fraction. Then, change the operation to multiplication:

\(\displaystyle \frac{45}{4} \ast \frac{5}{27}=\)

Reduce where possible and multiply. Convert your answer into a mixed fraction.

First find the exponent value for each number:

\(\displaystyle 8^{3}\div 2^{2}=512 \div 4=\)

Then divide accordingly. The answer is 128.

First follow order of operations and solve on each side.

\(\displaystyle 11+39=12+28+2a\)

\(\displaystyle 50=40+2a\)

Then, subtract 40 from each side to leave only the variable:

\(\displaystyle 50-40=40+2a-40\)

\(\displaystyle 10=2a\)

Finally, divide both sides by 2.

\(\displaystyle 10\div 2=2a\div 2\)

The answer is \(\displaystyle 5=a\)