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    Exercise 8.2.1

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6th class > > Exercise 8.2.1

Exercise 8.2.1

1.Solve the following equations and check your results.

1.3x = 2x + 18

3x = 2x+18 : 3x-2x = 18 : x=.
Substuite x in equation.
3x=2x+18 : 3()=2()+18.
: 3x18 = 2x18 = =+18 : =.
LHS to RHS.

2.5t−3=3t−5

= 5t = 3t - 5 + 3 : 5t = 3t - 2 : 5t - 3t = - 2.
= 2t = -2 : t=−22 : t = .
Substitute T in equation.
= 5t-3 = 3t-5 : 5()-3 = 3()-5
= -5-3 = -3-5 : = .
LHS to RHS.

3.5x + 9 = 5 + 3x

Substitute 3x in both sides 5x - 3x+ 9 = 5 + 3x - 3x : 2x + 9 = 5
Subtract 9 from both sides 2x+9 - 9 = 5-9 : 2x = .
Divide both sides by 2 to slove : 2x2 = −42 : x = .
Substitute x in Equation.
= 5()+9 : 5+3() : -10+9 = 5-6 : =.
LHS to RHS.

4.4z+3=6+2z

subtract 2z from both sides 4z-2z+3 = 6+2z-2z : 2z+3=6.
substract 3 from both sides 2z+3-3=6-3 : 2z = 3.
Divide both sides by 2 2z2=32 : z = 32.
Substitute z in Equation.
= 4()+3 = 6+2() : 6+3 = 6+3 : =.
LHS to RHS.

5.2x-1=14-x

Add x to both sides 2x+x-1=14-x+x : 3x-=14.
Add 1 to both sides 3x-1+1 = 14+1 : 3x=.
Divide both sides by 3 3x3=153 : x=.
Substitute x in Equation.
2x-1=14-5 : 10-1=9 : =
LHS to RHS.

6.8x+4=3(x-1)+7

Distribute the 3 on the right side 8x+4=3x-3+7.
Combine like terms on the right side 8x+4=3x+4.
Subtract 3x from both sides 8x-3x+4 = 4 : 5x+4 = 4
subtract 4 from both sides 5x+4-4 = 4-4 : 5x = 0.
Divide both sides by 5 5x5=05 : x=.
8x+4=3(-1)+7 : 4=3(-1)+7 : 4=3(-1)+7 : 4=-3+7 : =.
LHS to RHS.

7.x=45(x+10)

Distribute 45 on the right side x = 45.x+45.10 : x = 45.10 : x = 45x+8.
Subtract 45x from both sides x-45x=8 : 15x=8.
Multiply both sides by 5 5.15x=5.8 : x=.
Substitute x in Equation.
40=45(40+10) : 40=45.50 : =.
LHS to RHS.

8.2x3+1=7x15+3

Subtract 1 from both sides 2x3+1-1=7x15+3-1 : 2x3 = 7x15+2.
Subtract 7x15 from both sides 2x3-7x15= 2
Find common denominator 15 - 10x15 - 7x15 = 2 : 3x15 = 2.
Simplify the Equation : 3x15=2 : x5 = 2.
Multiply both sides by 5, x = 2.5 : x = .
Substitute x in Equation.
= 2./3+1=7./15+3 : 203+1=7015+3
convert 7015 to a common denominator: 203+1=143+3 : 203+33= 143+93 : / = /
LHS to RHS.

9.2y+53=263-y

simplify the equation 2y+y+53=263 : 3y+53=263 : 3y=/
= 3y = 213 : 3y = 7 : y = /.
Substitute y in Equation.
= 2(7/3)+53= 26/3-(/) : 143 + 53 = 193 : /=/.
LHS to RHS.

10.3m=5m-85

Substract 5m from both sides 3m-5m = 5m-5m-85 : -2m=−85.
Divide both sides by -2 to slove for m -2m/-2=-(8/5)/-2 : m=/.
Substitute m in Equation.
3.4/5=5.4/5-8/5 : 12/5=20/5-8/5 : / = /.
LHS to RHS