3<5+6h<10 please do step by step

Mathematics

1 answer:

hram777 [196]3 years ago

4 0

Answer:

see explanation

Step-by-step explanation:

Given

3 < 5 + 6h < 10 ( subtract 5 from each interval )

- 2 < 6h < 5 ( divide each interval by 6 )

- $\frac{1}{3}$ < h < $\frac{5}{6}$

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10 subtracted from the quotient of a number and -3 is at least -1

Mazyrski [523]

10 subtracted from the quotient of a number and -3 is at least -1 is:

$\left(\frac{x}{-3}\right)-10\ge \:-1\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-27\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-27]\end{bmatrix}$

Solution:

Given statement is:

10 subtracted from the quotient of a number and -3 is at least -1

Quotient means reuslt of dividing two numbers

Let the number be "x"

quotient of a number and -3 = $\frac{x}{-3}$

Therefore,

10 subtracted from $\frac{x}{-3}$ is at least -1

at least means "less than or equal to"

Which is translated into algebraic expression as:

$(\frac{x}{-3}) - 10\geq -1$

Solve the above inequality

$\left(\frac{x}{-3}\right)-10\ge \:-1\\\\\mathrm{Add\:}10\mathrm{\:to\:both\:sides}\\\\\frac{x}{-3}-10+10\ge \:-1+10\\\\\mathrm{Simplify}\\\\\frac{x}{-3}\ge \:9\\\\Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)$

When we multiply or divide by negative number. we have to flip the inequality sign

$\frac{x\left(-1\right)}{-3}\le \:9\left(-1\right)\\\\\mathrm{Simplify}\\\\\frac{x}{3}\le \:-9\\\\\mathrm{Multiply\:both\:sides\:by\:}3\\\\\frac{3x}{3}\le \:3\left(-9\right)\\\\\mathrm{Simplify}\\\\x\le \:-27$