Question

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

Answer 1

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.

Answer 2

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