If n=4x−3, then what is the value of x when n=11?

the tens digit of a two digit number is 5 greater the units digit. If you subtract double the reversed number from it, the resul

likoan [24]

Given:

The tens digit of a two digit number is 5 greater the units digit.

If you subtract double the reversed number from it, the result is a fourth of the original number.

To find:

The original number.

Solution:

Let n be the two digit number and x be the unit digit. Then tens digit is (x+5) and the original number is:

$n=(x+5)\times 10+x\times 1$

$n=10x+50+x$

$n=11x+50$

Reversed number is:

$x\times 10+(x+5)\times 1=10x+x+5$

$x\times 10+(x+5)\times 1=11x+5$

If you subtract double the reversed number from it, the result is a fourth of the original number.

$11x+50-2(11x+5)=\dfrac{1}{4}(11x+50)$

$11x+50-22x-10=\dfrac{1}{4}(11x+50)$

$40-11x=\dfrac{1}{4}(11x+50)$

Multiply both sides by 4.

$160-44x=11x+50$

$160-50=11x+44x$

$110=55x$

Divide both sides by 55.

$\dfrac{110}{55}=x$

$2=x$

The unit digit is 2. So, the tens digit is $2+5=7$ .

Therefore, the original number is 72.

6 0

3 years ago

What is the answer to this solution. -7r−4≥ 4r+2

tia_tia [17]

Answer:

The solution is:

$-7r-4\ge \:\:4r+2\quad \::\quad \:\begin{bmatrix}\mathrm{Solution:}\:&\:r\le \:\:-\frac{6}{11}\:\\ \:\:\mathrm{Decimal:}&\:r\le \:\:-0.54545\dots \:\\ \:\:\mathrm{Interval\:Notation:}&\:(-\infty \:\:,\:-\frac{6}{11}]\end{bmatrix}$

Please check the attached line graph below.

Step-by-step explanation:

Given the expression

$-7r-4\ge \:4r+2$

Add 4 to both sides

$-7r-4+4\ge \:4r+2+4$

Simplify

$-7r\ge \:4r+6$

Subtract 4r from both sides

$-7r-4r\ge \:4r+6-4r$

Simplify

$-11r\ge \:6$

Multiply both sides by -1 (reverses the inequality)

$\left(-11r\right)\left(-1\right)\le \:6\left(-1\right)$

Simplify

$11r\le \:-6$

Divide both sides by 11

$\frac{11r}{11}\le \frac{-6}{11}$

Simplify

$r\le \:-\frac{6}{11}$

Therefore, the solution is:

$-7r-4\ge \:\:4r+2\quad \::\quad \:\begin{bmatrix}\mathrm{Solution:}\:&\:r\le \:\:-\frac{6}{11}\:\\ \:\:\mathrm{Decimal:}&\:r\le \:\:-0.54545\dots \:\\ \:\:\mathrm{Interval\:Notation:}&\:(-\infty \:\:,\:-\frac{6}{11}]\end{bmatrix}$

Please check the attached line graph below.