Replacement and Solution Set

Q.

If $f\left(x\right)=\frac{\left(x-1\right)}{4}+\frac{{\left(x-1\right)}^3}{12}+\frac{{\left(x-1\right)}^5}{20}+\frac{{\left(x-1\right)}^7}{28}+......$where $0<x<2$ then $f\left(x\right)$ is equal to.

1. $\frac{1}{4x\left(2-x\right)}$

2. $\frac{1}{4{\left(x-2\right)}^2}$

3. $\frac{1}{2-x}$

4. $\frac{1}{2+x}$

Q. Question 1
Amina thinks of a number and subtracts $\frac{5}{2}$ from it. She multiplies the result by 8 .The result now obtained is 3 times the same number she thought of. What is the number?

Q.

If the replacement set is the set of natural numbers (N), then find the solution set for the given inequation $1+9x\ge x+81$.

1. $\{x:x\ge 10,x\epsilon W)$
2. $\{x:x>10,x\epsilon W)$
3. $\{x:x\ge 11,x\epsilon R)$
4. $\{x:x\le 10,x\epsilon W)$

Q.

Solve the following problems:

The numerator of a fraction is $4$ less than its denominator. If both numerator and denominator are divided by $4$, the fraction becomes $\frac{2}{3}$. Find the fraction.

Q.

How do you solve and write the following in interval notation:$-12<3-3x\le 15$?

Q.

Solve the following inequation:
$-6-4x<10;xϵZ$.

1. $x\ge 4$
2. $x<4$
3. $x>-4$
4. $x\le -4$

Q.

The solution set for the inequation -3 $\le$ x $\le$ 3, x $\in$ I is

1. {-2, -1, 0, 1, 2}

2. {-3, -2, -1, 0, 1, 2, 3}

3. {0, 1, 2, 3}

4. {-3, -2, -1, 0}

Q.

If the replacement set is the set of Natural numbers, find the solution set for the given linear inequation 9x + 4 < 67.

1. $\{1,2,3,4,5,6\}$

2. $\{2,3,4,5,6,7\}$

3. $\{5,7,8\}$

4. $\{0,1,2,3\}$

Q.

Find the solution set such that $xϵN$ and $4x+1<9$

1. {0, 1, 2}

2. {1}

3. {1, 2}

4. {8, 9}

Q.

Write the following statement in the form of equation:
$Quotientofbby4increasedby6gives10.$

Q.

Solve the following inequation and find the cardinality of the solution set.

$\frac{2x+3}{3}\ge \frac{3x-1}{4}$ where x is positive even integer.

1. 6

2. 7

3. 8

4. 5

Q.

Find the range of values of x which satisfy $\frac{-1}{3}\le \frac{x}{2}-\frac{4}{3}<\frac{1}{6}$, where x ϵ real number.

1. $2<x<3$
2. $2\le x\le 3$
3. $3\le x<2$
4. $2\le x<3$

Q.

Given
$P=\{x:6<3x-9<12,x\in R\}Q=\{x:-1\le 3+4x\le 35,x\in I\}$
Write down the elements of $P\cap Q$

1. {-1, 0, 1, 2, 3, 4, 5, 6, 7, 8}

2. {-1, 0, 1, 2, 3}

3. {6}

4. {5}

Q.

Find the solution set for $x+\frac{5}{2}<-\frac{5}{2}+5x$; where $xϵZ$

1. $x<2$

2. $x<-2.5$

3. $x>2$

4. $x<-2$

Q.

Given $3+\frac{a}{3}<5+\frac{a}{4}$ ; where $aϵw,a$ can take the value of $24.$

1. True

2. False

Q.

Find the solution set of the given inequation $-8-\frac{x}{4}>1;xϵR$.

1. $x>-36$
2. $x\le 36$
3. $x<-36$
4. $x\ge 36$

Q.

Find the solution set for $x+\frac{5}{2}<-\frac{5}{2}+5x$; where $xϵZ$

1. x < 2

2. x > 2

3. x < -2.5

4. x < -2

Q.

Find the number of values of x satisfying

$3x-3\le 7x+5and5-x\ge \left(\frac{x}{4}\right)-\left(\frac{5}{4}\right),wherexϵN.$

1. 4

2. 6

3. 5

4. 7

Q.

The value of x in 8x+6 > 86 is :

1. equal to 10

2. greater than 10

3. equal to 8

4. less than 8

Q.

Write the inequality modeled by the algebra tiles. Then solve the inequality using algebra tiles. Check your answer using properties of inequality.

Q.

Find the least value $x$ that satisfies the following inequation:
$-27+2x\le 9$ ; $xϵN$

1. 18
2. 1
3. 0
4. 19

Q.

If the replacement set is the set of whole numbers, solve: $7-3x\ge \frac{-1}{2}$.

1. {2, 3, 4, 5}
2. {6, 7, 8}
3. {9, 10, 11}
4. {0, 1, 2}

Q.

Solve the following equations and check your result:

$\frac{\mathrm{a}}{8}+\frac{5}{4}=2$

Q.

Solve the following inequation and represent the solution set on the number line, $x-3-\frac{1}{7}\left(5x-17\right)>0,\forall x\in \mathrm{ℝ}$.