Tag: reducing simple equations to simpler form

Questions Related to reducing simple equations to simpler form

If $\sqrt {x-1}-\sqrt {x + 1} + 1= 0$, then $4x$ equals

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $5$

  2. $4$

  3. $3$

  4. $2$

Show answer
Correct Option: A
Explanation:

$\sqrt {x-1}-\sqrt {x+1}+1=0$
or $\sqrt {x-1}=\sqrt {x+1}=-1$
Squaring, we get
$x-1=x+1+1-2\sqrt {x+1}$
or $2\sqrt {x+1}=3$
or $4(x+1)=9$ or $4x=9-4=5$

Seamus has $3$ times as many marbles as Ronit, and Taj has $7$ times as many marbles as Ronit. If Seamus has $s$ marbles then, in terms of $s$, how many marbles do Seamus, Ronit and Taj have together?

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $\cfrac{3}{7}s$

  2. $\cfrac{7}{3}s$

  3. $\cfrac{11}{3}s$

  4. $7s$

  5. $11s$

Show answer
Correct Option: C
Explanation:
The problem will be easier to solve if you can choose numbers that will give you all integers as you solve. both Seamus and Taj have a multiple of the number of marbles that Ronit has, so begin by picking for Ronit, not for Seamus.
If Ronit has $2$ marbles, then Seamus has $(3)(2)=6$ marbles and Taj has $(7)(2)=14$ marbles. Together, the three have $22$ marbles.
plug $s=6$ into the answer (remember that the problem asks about Seamus's starting number, not Ronit's and look for a match of $22$:
(A) $\cfrac{3}{7}s=$ not an integer
(B) $\cfrac{7}{3}s=\cfrac{7}{3}(6)=14$. Not a match
(C) $\cfrac{11}{3}s=\cfrac{11}{3}(6)=22$. Match!!
(D) $7s=42$. Not a match
(E) $11s=$ Too large
Alternately, you can use an algebraic approach. Begin by translating the first sentence into equations:
$s=3r$
$t=7r$
The question asks for the sum of the three:
$s+r+t=$?
The answer use only $s$, so figure out how to substitute to leave only $s$ in the equation
$r=\cfrac{s}{3}$
$t=7r=7(\cfrac{s}{3})$
Substitute those into the equation
$s+r+t$
$s+\cfrac{s}{3}+7(\cfrac{s}{3})$
$\cfrac{3s}{3}+\cfrac{s}{3}+\cfrac{7s}{3}$
$\cfrac{11s}{3}$
The correct answer is (C)

Solve the equation: $\dfrac{2z}{1-z}=6$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $z = \dfrac{1}{4}$

  2. $z = \dfrac{3}{4}$

  3. $z = \dfrac{2}{4}$

  4. $z = \dfrac{3}{7}$

Show answer
Correct Option: B
Explanation:

Given, $\dfrac{2z}{1-z}=6$
On multiplying both sides by $1 - z$, we get
$2z = 6(1 - z)$
$2z = 6 - 6z$
$8z = 6$
$z = \dfrac{3}{4}$

Solve the equation: $\dfrac{7x - 3}{3x}=2$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $x=3$

  2. $x=2$

  3. $x=1$

  4. $x=-1$

Show answer
Correct Option: A
Explanation:

$\dfrac{7x - 3}{3x}=2$
$7x - 3 = 6x$
On transposing $6x$ to the L.H.S and $3$ to the R.H.S we obtain
$7x - 6x = 3$
$x = 3$

Find the value of $ p$ in the linear equation: $4p + 2 = 6p + 10$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $p=-4$

  2. $p=-3$

  3. $p=-2$

  4. $p=-1$

Show answer
Correct Option: A
Explanation:

$4p + 2 = 6p + 10$

On transposing $4p+ 2$ to the R.H.S we obtain
$6p - 4p + 10 - 2 = 0$
$2p + 8 = 0$
$2p = -8$
$p = -4$

Solve the equation: $\dfrac{x+2}{2x}=1$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $x=2$

  2. $x=3$

  3. $x=4$

  4. $x=5$

Show answer
Correct Option: A
Explanation:

Given, $\dfrac{x+2}{2x}=1$
Multiplying both sides by $2x$, we obtain

$x + 2 = 2x$
$2x - x = 2$
$x = 2$

Reduce the following linear equation: $2x + 5 = 3$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $x=1$

  2. $x=-1$

  3. $x=0$

  4. $x=2$

Show answer
Correct Option: B
Explanation:

Given, $2x + 5 = 3$
On transposing $5$ to the R.H.S, we obtain 
$2x = 3 - 5$
$2x = -2$
$x = -1$

Calculate the value of $2x+y$, if $\dfrac{1}{2}x=5-\dfrac{1}{4}y$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $20$

  2. $-20$

  3. $10$

  4. $-10$

Show answer
Correct Option: A
Explanation:

Given, $\dfrac{1}{2}x=5-\dfrac{1}{4}y$

On multiplying both the sides by $4$, we get
$\Rightarrow 2x=20-y$

Adding $y$ on both the sides,
$\Rightarrow 2x+y=20$

Solve the following equation for the value of $x$: $6\sqrt [ 3 ]{ x } -24=6$.

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $25$

  2. $5$

  3. $100$

  4. $125$

Show answer
Correct Option: D
Explanation:

$6\sqrt[3]{x}-24=6$

$\Rightarrow 6\sqrt[3]x=6+24=30$
$\Rightarrow \sqrt[3]x=\dfrac{30}{6}=5$
Taking cube on both sides, we get
$x=5^3=125$

Solve for $x$:
$\dfrac {7}{3x + 4} = \dfrac {7}{6x - 2}$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $-2$

  2. $-1$

  3. $0$

  4. $2$

Show answer
Correct Option: D
Explanation:

Given,
$\dfrac { 7 }{ 3x+4 } =\dfrac { 7 }{ 6x-2 } $
$\Rightarrow 42x-14=21x+28$
$\Rightarrow 42x-21x=28+14$
$\Rightarrow 21x=42$
$\Rightarrow x=2$