Question

Drag a statement or reason to each box to complete the proof.



If 5(x+6)=x+38, then x=2.

Answer 1

See the attached picture:

Answer 2

Answer:

Given an equation: $5(x+6)=x+38$

Distributive Property of equality tells us that the multiplication over addition can be used when you multiply a number by a sum.

i.e $a\cdot(b+c)=a\cdot b+a\cdot c$

Apply distributive property on term 5(x+6) i.e,

$5(x+6)=5\cdot x+5\cdot 6 =5x+30$

Then, the equation become;

5x+30=x+38

Subtraction Property of equality states that you subtract the same number from both sides of an equation

Subtract 30 from both sides of an equation:

5x+30-30=x+38-30

On simplifying we get;

5x=x+8

Now, subtract x from side of the equation:

5x-x=x+8-x

Simplifying:

4x=8

Division Property of equality tells us that divide the same number from both side of an equation:

Divide 4 on both sides of an equation;

$\frac{4x}{4} =\frac{8}{4}$

Simplifying we get;

x=2