Question

Fill in the missing work and justification for step 3 when solving 2(x + 1) = 10. Step Work Justification 1 2(x + 1) = 10 Given 2 2x + 2 = 10 Distributive Property 3 4 2x = 8 Simplify 5 two times x over two equals eight over two Division Property of Equality 6 x = 4 Simplify 2x + 2 + 2 = 10 + 2; Addition Property of Equality 2x + 2 − 2 = 10 − 2; Subtraction Property of Equality (2x + 2)(2) = 10(2); Multiplication Property of Equality the quantity two times x plus two all over two equals ten over two; Division Property of Equality

Answer 1

Answer:

x=4

Step-by-step explanation:

2(x+1)=10

Distributive properties

a*(b+c)=(a*b)+(a*c)

Using distributive properties

Then

2*(x+1)=(2*x)+(2*1)

2*(x+1)=2x+2

Now, commutative properties

a*b=b*a

Addition is cumulative

a+(-b)=(-b)+a

Therefore applying to 2x+2

2x+2+(-2)=2x+(-2)+2

Then, applying to the equation

2x+2+(-2)=10+(-2), +×-=-

2x+2 -2=10-2

2x=8

Using division properties

ax=b

If a is none zero

Then ax/a=b/a

Therefore x=b/a

Applying that to 2x=8

2x=8. Divide both side by 2 which is none zero

2x/2= 8/2

x=4

Answer 2

Answer:

2(x + 1) = 10

2x + 2 = 10

2x +2 -2 = 10 - 2

2x = 10(Step 3)

2x/2 = 8/2

x = 4

Step-by-step explanation:

Given the equation:

2(x + 1) = 10

Open the bracket by multiplying 2 by (x + 1) - Distributive property

2x + 2 = 10;

Subtract 2 from both sides.

2x + 2 - 2 = 10 - 2( Subtraction property of equality)

2x = 8(Step 3 justified).

Divide both sides by 2

2x/2 = 8/2 - Division property of equality.

Therefore,

x = 4. (Solved)