How many solutions does these equations have? one, infinite or no solutions?

1. 7(y+3)=5y+8

2. 10+6x=2(5+3x)

3. 3x+5-x=2x+7

4. 4x-4=2x+8

Explanation:

1. 7(y+3)=5y+8

a)  Distributive property of multiplication over addtion:

b) Subtraction property of equalities:

c) Combine like terms:

d) Division property of division:

e) Conclusion: the equation has one solution.

2. 10 + 6x = 2(5+3x)

a) Distributive property of multiplication over addition:

b) Subtraction property of equality:

c) Simplify (combine like terms)

That is an identity, i.e. that is always true, no matter the value of x.

d) Conclusion: the equation has infinite solutions.

3. 3x + 5 - x = 2x + 7

a) Combine like terms:

b) Subtraction property of equalities:

c) Combine like terms (simplify)

That is always false, no matter the values of x.

d) Conclusion: the equation does not have any solutions.

4. 4x - 4 = 2x + 8

a) Subtraction property of equality

b) Combine like terms

c) Addtiion property of equalities:

d) Combine like terms (simplify)

e) Division property of equalities:

f) Conclusion: the equation has one solution

d

step-by-step explanation:

d

a = 3.14

b = 18

c = 18/5 or 3.6 or 3 3/5

step-by-step explanation: