Question

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

Answer 1

No solution

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) = (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,`

`(1)/(2)\cdot (8+20m)=(1)/(2)\cdot 8+(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