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Provide the missing statement and reasons for the following proof:

Given: 9(x+6)−41=75

Prove: x=62/9



Statement | Reason
-------------------------------------------------
S1. 9(x+6)-41=75 | R1.

S2. 9(x+6)=116 | R2.

S3. | R3. Distributive Property

S4. 9x=62 | R4.

S5. x=62/9 | R5.

----------------------------------------------------

Sagot :

The missing statement for the proof is;

Statement 3;S3 : 9x + 54 = 116

The missing reasons for the proofs are;

R1; Given

R2; Using Addition property of inequality

R3; Distributive property

R4; Using subtraction property of inequality

R5; Using Division property of inequality

We are given the equation;

9(x + 6) − 41 = 75

Step 2;

Using addition property of equality, we add 41 to both sides;

9(x + 6) - 41 + 41 = 75 + 41

9(x + 6) = 116

Step 3;

Using distributive property to distribute 6 over the items in the bracket to get;

9x + 54 = 116

  • Step 4; Using subtraction property of equality, we subtract 54 from both sides;

       9x + 54 - 54 = 116 - 54

       9x = 62

  • Step 5; Using division property of equality, we divide both sides by 9 to get;

       9x/9 = 62/9

       x = 62/9

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