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3 years ago

-9m - 4 = -7m + 6 solve for m

Mathematics

1 answer:

astraxan [27]3 years ago

4 0

Answer:

m = -5

Step-by-step explanation:

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Leviafan [203]

Answer:

See explanation.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
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Left to Right

Algebra I

Functions
Function Notation

Calculus

Limits

Right-Side Limit: $\displaystyle \lim_{x \to c^+} f(x)$
Left-Side Limit: $\displaystyle \lim_{x \to c^-} f(x)$

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = \left \{ {{\sqrt{x + 1}, \ x < 3} \atop {5 - x, \ x \geq 3}} \right.$

Step 2: Find Right Limit

Substitute in variables [Right-Side Limit]: $\displaystyle \lim_{x \to 3^+} 5 - x$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle \lim_{x \to 3^+} 5 - x = 5 - 3$
Subtract: $\displaystyle \lim_{x \to 3^+} 5 - x = 2$

∴ the right-side limit equals 2.

Step 3: Find Left Limit

Substitute in variables [Left-Side Limit]: $\displaystyle \lim_{x \to 3^-} \sqrt{x + 1}$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{3 + 1}$
[√Radical] Add: $\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{4}$
[√Radical] Evaluate: $\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = 2$

∴ the left-side limit equals 2.

Step 4: Find Limit

The right and left-side limits are equal.

∴ $\displaystyle \lim_{x \to 3} f(x) = 2$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

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