Mathematics, 27.06.2021 20:30, ben5445

Solve the inequality for x
3^(6x+18)<27^(3x)

Answers: 1

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Answers

answered: lorenzo1beaton

$\displaystyle x 6$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/CoefficientsFactoring

Algebra II

Exponential Rule [Powering]: $\displaystyle (b^m)^n = b^{m \cdot n}$ Solving exponential equations

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle 3^{6x + 18} < 27^{3x}$

Step 2: Solve for x

Rewrite: $\displaystyle 3^{6x + 18} < 3^{3(3x)}$ Set: $\displaystyle 6x + 18 < 3(3x)$ Factor: $\displaystyle 3(2x + 6) < 3(3x)$ [Division Property of Equality] Divide 3 on both sides: $\displaystyle 2x + 6 < 3x$ [Subtraction Property of Equality] Subtract 3x on both sides: $\displaystyle -x + 6 < 0$ [Subtraction Property of Equality] Subtract 6 on both sides: $\displaystyle -x < -6$ [Division Property of Equality] Divide -1 on both sides: $\displaystyle x 6$

answered: randallmatthew5665

Step-by-step explanation:

When given the following equation;

3^(^6^x^+^1^8)

One is asked to solve for (). The inequality has exponents, hence, it appears daunting at first, however, the easiest way to deal with exponents is to bring them to the same base. This allows for one to have the ability to treat the exponents like an ordinary number. Since ( 27=3^3 ) one can rewrite ( 27^(^3^x^) ) as ( 3^3^*^(^3^x^) ). This is possible because raising a number to an exponent when it already has an exponent is the same as multiplying the two exponents. Rewrite the inequality in this format;