Download App

MATHS 3 Marks Question

Linear Equations in One Variable · Gujarat Board (GSEB) STD 8 (GSEB - English Medium). 11 questions.

Questions

3 Marks Question

🎯

Test yourself on this topic

11 questions · timed · auto-graded

Question 13 Marks
Solve the following equations :
$3 m=5 m-\frac{8}{5}$
Answer
We have, $\quad \frac{2 x}{3}+1=\frac{7 x}{15}+3$
$\Rightarrow \quad \frac{2 x}{3}-\frac{7 x}{15}=3-1\quad$ [transposing $\frac{7 x}{15}$ to LHS and 1 to RHS]
$\Rightarrow \quad \frac{10 x-7 x}{15}=2 \quad[\because$ LCM of 3 and 15 is 15$]$
$\Rightarrow \quad \frac{3 x}{15}=2$
$\Rightarrow \quad \frac{3 x}{15} \times 5=2 \times 5 \quad$ [multiplying both sides by 5]
$\Rightarrow \quad \frac{15 x}{15}=2 \times 5 \Rightarrow x=2 \times 5$
$\Rightarrow \quad x=10$, which is the required solution.
Check For $x=10$
LHS $=\frac{2(10)}{3}+1=\frac{23}{3}$
RHS $=\frac{7(10)}{15}+3=\frac{23}{3}$
$\therefore \quad$ LHS $=$ RHS $\quad$ [as required]
View full question & answer→
Question 23 Marks
Solve the following equations :
$2 y+\frac{5}{3}=\frac{26}{3}-y$.
Answer
We have, $\quad \frac{2 x}{3}+1=\frac{7 x}{15}+3$
$\Rightarrow \quad \frac{2 x}{3}-\frac{7 x}{15}=3-1\quad$ [transposing $\frac{7 x}{15}$ to LHS and 1 to RHS]
$\Rightarrow \quad \frac{10 x-7 x}{15}=2 \quad[\because$ LCM of 3 and 15 is 15$]$
$\Rightarrow \quad \frac{3 x}{15}=2$
$\Rightarrow \quad \frac{3 x}{15} \times 5=2 \times 5 \quad$ [multiplying both sides by 5]
$\Rightarrow \quad \frac{15 x}{15}=2 \times 5 \Rightarrow x=2 \times 5$
$\Rightarrow \quad x=10$, which is the required solution.
Check For $x=10$
LHS $=\frac{2(10)}{3}+1=\frac{23}{3}$
RHS $=\frac{7(10)}{15}+3=\frac{23}{3}$
$\therefore \quad$ LHS $=$ RHS $\quad$ [as required]
View full question & answer→
Question 33 Marks
Solve the following equations :
$\frac{2 x}{3}+1=\frac{7 x}{15}+3.$
Answer
We have, $\quad \frac{2 x}{3}+1=\frac{7 x}{15}+3$
$\Rightarrow \quad \frac{2 x}{3}-\frac{7 x}{15}=3-1\quad$ [transposing $\frac{7 x}{15}$ to LHS and 1 to RHS]
$\Rightarrow \quad \frac{10 x-7 x}{15}=2 \quad[\because$ LCM of 3 and 15 is 15$]$
$\Rightarrow \quad \frac{3 x}{15}=2$
$\Rightarrow \quad \frac{3 x}{15} \times 5=2 \times 5 \quad$ [multiplying both sides by 5]
$\Rightarrow \quad \frac{15 x}{15}=2 \times 5 \Rightarrow x=2 \times 5$
$\Rightarrow \quad x=10$, which is the required solution.
Check For $x=10$
LHS $=\frac{2(10)}{3}+1=\frac{23}{3}$
RHS $=\frac{7(10)}{15}+3=\frac{23}{3}$
$\therefore \quad$ LHS $=$ RHS $\quad$ [as required]
View full question & answer→
Question 43 Marks
Solve the following equations :
$8 x+4=3(x-1)+7.$
Answer
We have,
$8 x+4=3(x-1)+7$
$\Rightarrow \quad 8 x+4=3 x-3+7$
$\Rightarrow \quad 8 x+4=3 x+4$
$\Rightarrow \quad 8 x-3 x=4-4\quad$ [transposing $3 x$ to LHS and 4 to RHS]
$\Rightarrow \quad 5 x=0$
$\Rightarrow \quad x=\frac{0}{5} \quad$ [dividing both sides by 5]
$\therefore x=0$, which is the required solution.
Check For x = 0,
$L H S=8(0)+4=4$
RHS $=3(0-1)+7=4$
$\therefore \quad$ LHS $=$ RHS $\quad$ [as required]
View full question & answer→
Question 53 Marks
Solve $\frac{x}{2}+\frac{x}{4}+\frac{x}{5}+10000=x$.
Answer
We have, $\frac{x}{2}+\frac{x}{4}+\frac{x}{5}+10000=x$
$\Rightarrow \quad \frac{x}{2}+\frac{x}{4}+\frac{x}{5}-x=-10000\quad$ [transposing $x$ to LHS and 10000 to RHS]
$\Rightarrow \quad \frac{10 x+5 x+4 x-20 x}{20}=-10000$
$\Rightarrow \quad \frac{19 x-20 x}{20}=-10000$
$\Rightarrow \quad \frac{-x}{20}=-10000$
$\therefore \quad x=200000$
View full question & answer→
Question 63 Marks
For what value of $x$, the perimeter of shape is 77 cm?
Image
[Hint Perimeter = add the sides of the shape]
Answer
We have, perimeter $=77 cm$
$\therefore(x+1)+(x+2)+(2 x+2)+(2 x+1)+(x+1)=77$
$\Rightarrow \quad 7 x+7=77 \Rightarrow 7 x=77-7$
$\Rightarrow \quad 7 x=70 \Rightarrow x=70 \times \frac{1}{7} \Rightarrow x=10$
Hence, the required value of $x$ is 10 cm.
View full question & answer→
Question 73 Marks
Solve for $x, \frac{3 x-5}{17}+\left[\frac{11-x}{76}-\frac{3}{4}\right]=\frac{4+x}{2}-13$.
Answer
We have, $\frac{3 x-5}{17}+\left[\frac{11-x}{76}-\frac{3}{4}\right]=\frac{4+x}{2}-13$
$\Rightarrow \quad \frac{3 x}{17}-\frac{5}{17}+\frac{11}{76}-\frac{x}{76}-\frac{3}{4}=2+\frac{x}{2}-13$
$\Rightarrow \quad \frac{3 x}{17}-\frac{x}{76}-\frac{x}{2}=-11+\frac{5}{17}-\frac{11}{76}+\frac{3}{4}$
$\Rightarrow \frac{456 x-34 x-1292 x}{2584}=\frac{-56848+1520-748+3876}{5168}$
$\Rightarrow \quad \frac{456 x-1326 x}{2584}=-\frac{52200}{5168}$
$\Rightarrow \quad \frac{-870 x}{2584}=\frac{-52200}{5168}$
$\Rightarrow \quad x=\frac{-52200}{5168} \times\left(\frac{-2584}{870}\right)$
$=\frac{60}{2}=30$
View full question & answer→
Question 83 Marks
Simplify and solve the following linear equation $3(5 y-7)-2(9 y-11)=4(8 y-13)-17$
Also, check your answer.
Answer
We have, $3(5 y-7)-2(9 y-11)=4(8 y-13)-17$
$15 y-21-18 y+22=32 y-52-17$
$\Rightarrow \quad-3 y+1=32 y-69$
$\Rightarrow \quad 1+69=32 y+3 y\quad$ [transposing -69 to LHS and $-3 y$ to RHS ]
$\Rightarrow \quad 70=35 y \Rightarrow y=2$
Check On putting $y=2$ in both sides of the given equation, we get
$3(5 \times 2-7)-2(9 \times 2-11)=4(8 \times 2-13)-17$
$\Rightarrow \quad 3(10-7)-2(18-11)=4(16-13)-17$
$\Rightarrow \quad 3 \times 3-2 \times 7=4 \times 3-17$
$\Rightarrow$ $\quad 9-14=12-17 \Rightarrow-5=-5$
$\Rightarrow \quad$ LHS $=$ RHS
So, $y=2$ is solution of the given linear equation.
View full question & answer→
Question 93 Marks
Solve $\frac{3 t-2}{3}+\frac{2 t+3}{2}=t+\frac{7}{6}$
Answer
We have, $\frac{3 t-2}{3}+\frac{2 t+3}{2}=t+\frac{7}{6}$
$\Rightarrow \quad \frac{3 t-2}{3}+\frac{2 t+3}{2}-\frac{t}{1}=\frac{7}{6}\quad$ [transposing $t$ to LHS]
$\Rightarrow \frac{2 \times(3 t-2)+3 \times(2 t+3)-6 \times t}{6}=\frac{7}{6}$
$\Rightarrow \quad \frac{6 t-4+6 t+9-6 t}{6}=\frac{7}{6}$
$\Rightarrow \quad \frac{6 t+5}{6}=\frac{7}{6}$
$\Rightarrow \quad(6 t+5)=\frac{7 \times 6}{6}\quad$ [multiplying both sides by 6]
$\Rightarrow \quad 6 t+5=7$
$\Rightarrow \quad 6 t=7-5=2\quad$ [transposing 5 to RHS]
$\therefore \quad t=\frac{2}{6}=\frac{1}{3}$
View full question & answer→
Question 103 Marks
Show that $y=4$ is a solution of the equation
$ y+7-\frac{8 y}{3}=\frac{17}{6}-\frac{5 y}{8} $
Answer
On substituting $y=4$ in the given equation, we get
LHS $=4+7-\frac{8 \times 4}{3}=11-\frac{32}{3}=\frac{33-32}{3}=\frac{1}{3}$
and RHS $=\frac{17}{6}-\frac{5 \times 4}{8}=\frac{17}{6}-\frac{20}{8}=\frac{68-60}{24}=\frac{8}{24}=\frac{1}{3}$
Thus, LHS = RHS
So, $y=4$ is the solution of the given equation.
View full question & answer→
Question 113 Marks
Find the solution of the equation $5(3+y)=20+y$.
Answer
We have, $5(3+y)=20+y$
$\Rightarrow \quad 15+5 y=20+y$
$\Rightarrow \quad 5 y-y=20-15\quad$ [transposing $y$ to LHS and 15 to RHS]
$\Rightarrow \quad 4 y=5$
$\therefore \quad y=\frac{5}{4} \quad$ [dividing both sides by 4]
Thus, solution of the given equation is $\frac{5}{4}$.
View full question & answer→
Generate Paper FreeAll Linear Equations in One Variable topics