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umka21 [38]
3 years ago
5

Determine whether the equation 5(1+2m)=1/2(8+20m) has one solution, no solution, or infinitely many solutions.

Mathematics
2 answers:
abruzzese [7]3 years ago
5 0

Answer:

No solution

Step-by-step explanation:

There are three cases in a one variable equation of degree one,

Equation has one solution : if after solving it we get a solution,

Equation has infinitely many solution :  if after solving the equation we get a true statement,

Equation has no solution : if after solving it we get a false statement.

Given equation,

5(1+2m) = \frac{1}{2}(8 + 20m)

By distributive property,

5 + 10m = 4 + 10m

⇒ 5 = 4 ( FALSE )

Hence, the equation has no solution.

hichkok12 [17]3 years ago
3 0

1. Use the distributive property:

5\cdot (1+2m)=5\cdot 1+5\cdot 2m=5+10m,

\dfrac{1}{2}\cdot (8+20m)=\dfrac{1}{2}\cdot 8+\dfrac{1}{2}\cdot 20m=4+10m.

Then

5+10m=4+10m.

2. Separate terms with m in left side and without m in right side:

10m-10m=4-5,\\ \\0=-1.

This expression is false for all values of x, then the equation doesn't have solutions.

Answer: no solution

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