Does x < 4 mean the same thing as 4 > x

Yes

Step-by-step explanation:

In the first case, x < 4 simply says x is less than 4, while in the second case 4 > x means that 4 is greater than x. Either way we can understand that 4 is greater than x. So, both x < 4 and 4 > x mean the same thing.

Yes,

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by an exponent that is a rational number).[1] For example, 3x2 − 2xy + c is an algebraic expression. Since taking the square root is the same as raising the power  1/2,  is also an algebraic expression.

By contrast, transcendental numbers like π and e are not algebraic, since they are not derived from integer constants and algebraic operations. Usually, Pi is constructed as a geometric relationship, and the definition of e requires an infinite number of algebraic operations.

A rational expression is an expression that may be rewritten to a rational fraction by using the properties of the arithmetic operations (commutative properties and associative properties of addition and multiplication, distributive property, and rules for the operations on the fractions). In other words, a rational expression is an expression that may be constructed from the variables and the constants by using only the four operations of arithmetic. Thus,  is a rational expression, whereas  is not.

A rational equation is an equation in which two rational fractions (or rational expressions) of the form  are set equal to each other. These expressions obey the same rules as fractions. The equations can be solved by cross-multiplying. Division by zero is undefined, so that a solution causing formal division by zero is rejected.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

a

step-by-step explanation:

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