Answer:
- 1. 7(y + 3) = 5y+8: <u>one solution</u>
- 2. 10 + 6x= 2(5+3x): <u>infinite solutions</u>
- 3. 3x + 5 - x=2x + 7: <u>no solutions</u>
- 4. 4x - 4 = 2x + 8: <u>one solution.</u>
Explanation:
<u>1. 7(y+3)=5y+8</u>
<u></u>
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.
<u>2. 10 + 6x = 2(5+3x)</u>
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.
<u>3. 3x + 5 - x = 2x + 7</u>
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.
<u>4. 4x - 4 = 2x + 8</u>
<u></u>
a) Subtraction property of equality
- 4x - 2x - 4 = 2x - 2x + 8
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
