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Evaluate the following expression:
[tex]\[ 14 \div (-6 - 4 + 3) + \left[ 15 \div (-7 + 2) - 9 \right] \div 6 \][/tex]

Sagot :

GinnyAnswer
Sure! Let's solve the expression step-by-step:

[tex]\[ 14 \div (-6 - 4 + 3) + \left[ 15 \div (-7 + 2) - 9 \right] \div 6 \][/tex]

### Step 1: Simplify the Inner Expressions

Start with the inner expressions:

1. Simplify [tex]\(-6 - 4 + 3\)[/tex]:
[tex]\[ -6 - 4 = -10 \][/tex]
[tex]\[ -10 + 3 = -7 \][/tex]

So, we have:
[tex]\[ 14 \div (-7) + \left[ 15 \div (-7 + 2) - 9 \right] \div 6 \][/tex]

2. Simplify [tex]\(-7 + 2\)[/tex]:
[tex]\[ -7 + 2 = -5 \][/tex]

Now the expression becomes:
[tex]\[ 14 \div (-7) + \left[ 15 \div (-5) - 9 \right] \div 6 \][/tex]

### Step 2: Perform the Divisions

1. Calculate [tex]\(14 \div (-7)\)[/tex]:
[tex]\[ 14 \div (-7) = -2 \][/tex]

2. Calculate [tex]\(15 \div (-5)\)[/tex]:
[tex]\[ 15 \div (-5) = -3 \][/tex]

So our expression now looks like:
[tex]\[ -2 + \left[ -3 - 9 \right] \div 6 \][/tex]

### Step 3: Simplify Inside the Brackets

1. Simplify [tex]\(-3 - 9\)[/tex]:
[tex]\[ -3 - 9 = -12 \][/tex]

So, we have:
[tex]\[ -2 + \left[ -12 \right] \div 6 \][/tex]

### Step 4: Perform the Division

1. Calculate [tex]\(-12 \div 6\)[/tex]:
[tex]\[ -12 \div 6 = -2 \][/tex]

So the expression becomes:
[tex]\[ -2 + (-2) \][/tex]

### Step 5: Final Addition

1. Calculate [tex]\(-2 + (-2)\)[/tex]:
[tex]\[ -2 + (-2) = -4 \][/tex]

Therefore, the result of the expression is:

[tex]\[ \boxed{-4} \][/tex]
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