Question

"No solutions & all real numbers"

Solve each equation showing all work:

1.) -2(6 - 2x) = 4(-3 + x)

2.) 5 - 1(2x + 3) = -2(4 + x)

Answer 1

1.)
`-12+4x=-12+4x`

2.)
`2-2x \\eq -8-2x`

Explanation:

The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding all the products.

`a(b+c)=ab+ac`

For the first equation

`-2(6-2x)=4(-3+x)\\(-2)(6)+(-2)(-2x)=(4)(-3)+(4)(x)\\-12+4x=-12+4x`

For the second equation

`5-1(2x+3)=-2(4+x)\\5+((-1)(2x)+(-1)(3))= (-2)(4)+(-2)(x)\\5+(-2x-3) = -8+(-2x)\\5-2x-3=-8-2x\\2-2x \\eq -8-2x`

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