Exercise 8.3.1
Solve the following linear equations.
1.
Now,let's solve for x ,The denominators are 2,5,3,4.The LCM of these numbers is 60.
Multiply every term in the equation by 60 : 60.(x 2 1 5 x 3 1 4
subtracting 20x from both sides : 30x - 20x - 12 = 15. This Simplifies to : 10x-12 = 15.
Add 12 to both sides of the equation with x : 10x-12+12=15+12 , This simplifies to : 10x=27
Finally divide both sides by 10 : x=27 10
Substitute x in the equation
= x 2 1 5 x 3 1 4 27 10 1 2 1 5 27 10 1 3 1 4
= 27 − 4 20 54 + 15 60
2.
Simplify the equation as LCM is 12 : 6 n − 3 3 n + 2 5 n 12
= 6 n − 9 n + 10 n 12 6 n + n 12
Substitute n in Equation.
= n 2 3 n 4 5 n 6 36 2 3 x36 4 5 x36 6
2. x+7-
Simplify the equation LCM is 6.
Multiply every term in the equation : 6.(x+7-8 x 3 17 6 5 x 2
Distribute the 6 through the equation : 6x+42-6.8 x 3 17 6 5 x 2
Simplify each term : 6x - 16x+
Isolate the variable x by getting all x-terms : -10x+15x+42=17 : 5x+42 = 17.
Subtract 42 from both sides : 5x = -25.
Divide both sides by 5 to solve for x : x=− 25 5
Substitute x in Equation.
-5+7-(8(-5))/3 = 40 3 17 6 25 2 40 3 92 6
Convert 2 to a fraction with a a common denominator of 3 : 6 3 40 3 92 6 46 3 92 6
Simplify the right side : 92 6
4.
The LSD of of 3 and 5 is 15.
Multiply every term in the equation by 15 to eliminate the fractions:15((x-5)/3)=15((x-3)/5) : 5(x-5)=3(x-3).
Distribute the multiplication on both sides : 5x-25=3x-9 .
Isolate x on one side ,Subtract 3x from both sides : 5x - 3x - 25 =
Add 25 to both sides : 2x - 25 + 25 = -9 + 25 : 2x = 16.
Divide both sides by 2 to solve : x = 16 2
substitute x in Equation.
= (
5.
The LCD of 4 and 3 is 12.
Multiply evert term in the equation by 12 : 123 t − 2 4 2 t + 3 3 2 3
Simplifies to 3(3t-2)-4(2t+3) = 8-12t.
Distribute the multipliaction on both sides : 9t - 6 - 8t- 12= 8- 12t.
Combine like terms : t-18=8-12t.
Isolate t on one side : t + 12t - 18 = 8 : 13t - 18 =
Add 18 to both sides : 13t-18+18=8+18 : 13t = 26.
Divide both sides by 14 : t=26 13
Substitute t in Equation.
= 3 2 − 2 4 2 2 + 3 3 3 − 7 3 2 − 6 3
6.m-
Simplify the Equation : 2 m − m − 1 2 m − 2 3 2 m − m + 1 2 m − 2 3
= m + 1 2 m − 2 3 m + 1 2 3 − m − 2 3 m + 1 2 3 − m − 2 3
= m + 1 2 5 − m 3
= 5m+3=10 : 5m=10-3 : 5m=7 : m=
Substitute m in Equation
= 7 5 7 5 − 1 2 7 5 − 2 3
Simplify and solve the following linear equations.
7. 3(t – 3) = 5(2t + 1)
Simplify the equation 3t-9=5(2t+1) : 3t-9 = 10t+5 : 3t-10t-9=5
= -7t-9=5 : -7t = 5+9 : -7t=14 : t=
Substitute t in Equation.
= 3(-2-3)=5(2(-2)+1) : 3(-5)=5(-3) : LHS
8. 15(y – 4) –2(y – 9) + 5(y + 6) = 0
Simplify the equation : 15-6-2y+18+5y+30=0 : 15y-2y+5y-60+18+30=0 : 18y-12=0.
= 18y = 12 : y=
Substitute y in Equation.
= 15 2 3 − 4 2 2 3 − 9 5 2 3 + 6 15 x − 10 3 2 − 25 3 5 20 3
= − 150 3 50 3 100 3 − 150 + 50 + 100 3
9.3(5z-7)-2(9z-11)=4(8z-13)-17
Simplify the equation : 15z-21-18z+22=4(8z-13)-17 : -3z+1=4(8z-13)-17 : -3z+1=32z-69.
= -3z=32z-70 : -35z=-70.
So, z= : z =
Substitute z in Equation
= 3(5x2-7)-2(9x2-11)=4(8x2-13)-17 : 3 x 3 - 2 x 7 = 4 x 3 - 17 : LHS
10.0.25(4f – 3) = 0.05(10f – 9)
Simplify the equation : 25 100 5 100 1 4 1 20
= 4 f − 3 /4=10 f − 9 /20 : 20f(4f-3)=4(10f-9) .
= 80f-40f-60=-36 : 40f=-36+60 : f=24 40
Substitute f in Equation.
0.25(4x0.6-3)=0.05(10x0.6-9) : LHS
1. Given here are some figures.
Classify each ofthem on the basis of the following.
: Enter the numbers from the image according to the type of image.
(a).Simple Curve :
(b).Simple Closed Curve :
(c).Polygon :
(d).Convex Polygon :
(e).Concave Polygon :
2. What is a regular polygon?
State the name of a regular polygon of
(i) 3 sides :
(ii) 4 sides :
(iii) 6 sides :