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3 years ago

Find the solution set of the inequality: -3x + 8 < 15

Mathematics

1 answer:

telo118 [61]3 years ago

7 0

Hello from MrBillDoesMath!

Answer:

x > -7/3

Discussion:

-3x + 8 < 15 => add 3x to both sides

(-3x + 3x) + 8 < 15 + 3x => (-3x + 3x) = 0

8 < 15 + 3x => subtract 15 from both sides

8-15 < 3x => 8 - 15 = -7

-7 < 3x => divide both sides by 3

-7/3 < x

Thank You,

MrB

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Read 2 more answers

Given limit f(x) = 4 as x approaches 0. What is limit 1/4[f(x)]^4 as x approaches 0?

stepladder [879]

Answer:

$\displaystyle 64$

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Limit Rule [Variable Direct Substitution Exponential]: $\displaystyle \lim_{x \to c} x^n = c^n$

Limit Property [Multiplied Constant]: $\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \lim_{x \to 0} f(x) = 4$

Step 2: Solve

Rewrite [Limit Property - Multiplied Constant]: $\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4} \lim_{x \to 0} [f(x)]^4$
Evaluate limit [Limit Rule - Variable Direct Substitution Exponential]: $\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4}(4^4)$
Simplify: $\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = 64$