Given: -2(x - 4) = 2x + 12
Prove: x = -1
Statements
Reasons
1)
1)
2)
2) Distributive Property
3)
3)
4) -4x = 4
4)
5)
5) Division Property of Equality
1) -2(x - 4) = 2x + 12
2) -2x + 8 = 2x + 12 (Distributive Property)
3) -2x + 8 - 2x = 2x + 12 - 2x (Subtract 2x from both sides)
4) -4x + 8 = 12
5) -4x = 4 (Subtract 8 from both sides)
6) x = -1 (Division Property of Equality)
Statements:
1) -2(x - 4) = 2x + 12
2) Distributive Property: -2(x - 4) = -2x + 8
3) Simplify: -2x + 8 = 2x + 12
4) Subtract 2x from both sides: -4x + 8 = 12
5) Subtract 8 from both sides: -4x = 4
6) Divide both sides by -4: x = -1
Reasons:
1) Given
2) Distributive Property: -a(b + c) = -ab - ac
3) Simplify the expression
4) Subtract 2x from both sides to isolate the x term
5) Subtract 8 from both sides to isolate the constant term
6) Divide both sides by -4 to solve for x using the Division Property of Equality