The solutions for the given linear equations are:
7. 3(t - 3) = 5(2t + 1); solution is t = -2
8. 15(y - 4) - 2(y - 9) + 5(y + 6) = 0; solution is y = 2/3
9. 3(5z - 7) - 2(9z - 11) = 4(8z - 13) - 17; solution is z = 2
10. 0.25(4f - 3) = 0.05(10f - 9); solution is f = 0.6.
What is a linear equation?
An equation that has the highest degree of its variable as 1 is said to be a linear equation.
The general form is y = ax + b;
Where the power of the variable x is 1 and a, b are the real values.
Calculation:
Solving the given linear equations as follows:
7. Solving: 3(t - 3) = 5(2t + 1)
Applying distributive property a(b + c) = ab + ac;
⇒ 3t - 9 = 10t + 5
Writing like terms aside;
⇒ 3t - 10t = 5 + 9
⇒ -7t = 14
Dividing with -7 into both sides;
⇒ -7t/-7 = 14/-7
∴ t = -2
8. Solving: 15(y - 4) - 2(y - 9) + 5(y + 6) = 0
Applying distributive property a(b + c) = ab + ac;
⇒ 15y - 60 - 2y + 18 + 5y + 30 = 0
Adding the like terms;
⇒ 18y - 12 = 0
⇒ 18y = 12
Diving by 18 on both sides;
⇒ 18y/18 = 12/18
∴ y = 2/3
9. Solving: 3(5z - 7) - 2(9z - 11) = 4(8z - 13) - 17
Applying distributive property a(b + c) = ab + ac;
⇒ 15z - 21 - 18z + 22 = 32z - 52 - 17
Adding the like terms;
⇒ -3z + 1 = 32z - 69
Writing like terms aside;
⇒ 32z + 3z = 1 + 69
⇒ 35z = 70
Dividing by 35 into both sides;
⇒ 35z/35 = 70/35
∴ z = 2
10. Solving: 0.25(4f - 3) = 0.05(10f - 9)
Applying distributive property a(b + c) = ab + ac;
⇒ f - 0.75 = 0.5f - 0.45
Writing like terms aside;
⇒ f - 0.5f = 0.75 - 0.45
⇒ 0.5f = 0.3
Dividing by 0.5 into both sides;
⇒ 0.5f/0.5 = 0.3/0.5
∴ f = 0.6
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