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

Question

Mathematics

Madeline Snow

22 July, 07:58

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

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Answers (2)

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Charlie Sawyer · Answer 1

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

Mallory Buck · Answer 2

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)