Question

How many solutions for the equation 5X -10 =5(x-2)?

Answer 1

✦ Given that

• 5x - 10 = 5(x - 2)

✦ We need to find

• value of x

`\hrulefill`

`\longleftrightarrow\rm{5x-10=5(x-2)}`

`\longleftrightarrow\rm{5x-10=5x-10}`

`\longleftrightarrow\rm{5x-5x-10=-10}`

`\longleftrightarrow\rm{0x=-10+10}`

`\longleftrightarrow\rm{0x=0}`

`\longleftrightarrow\rm{0=0}`

`\longleftrightarrow\rm{Infinite \; solutions}`

Therefore the equation 5x - 10 = 5(x - 2) has infinite solutions.

`\hrulefill`

Answer 2

To find how many solutions this equation has, we can begin by distributing the 5 into the second equation:

5x - 10 = 5(x - 2) becomes 5x - 10

Because all of the values are the same on both sides of the equation, any real number can be inserted to receive the same output. Therefore, this equation has infinite (∞) solutions.