Question

Identify the property used in the first four steps to solve the equation 4(x-7)=2x-6 4x-28=2x-6 2x-28=-6 2x=22 x=11 the answer choices for each step are Distributive, addition property of equality and multiplication property of equalityd,a,a,m

Answer 1

Answer:

The reason of each steps are Distributive property, addition property of equality, addition property of equality and multiplication property of equality.

Step-by-step explanation:

Let a,b and c are real number.

According to distributive property

$a\cdot (b+c)=a\cdot b+a\cdot c$

Where, a,b and c are real number.

According to addition property of equality $a=b$ and $a+c=b+c$ are equivalent equations.

According to multiplicative property of equality $a=b$ and $ac=bc$ are equivalent equations.

The given equation is

$4(x-7)=2x-6$

$4(x)+4(-7)=2x-6$

$4x-28=2x-6$                 (Distributive Property)

Add -2x both sides.

$4x-28-2x=2x-6-2x$

$2x-28=-6$                     (Addition property of equality)

Add 28 both sides.

$2x-28+28=-6+28$

$2x=22$                     (Addition property of equality)

Multiply both sides by $\frac{1}{2}$

$2x\times \frac{1}{2}=22\times \frac{1}{2}$

$x=11$                         (Multiplication property of equality)