QuestionThe following expression equals -2 : $-2^{4} \div 4-4(x \div 6)+10$
Solve for the variable $x$ .

Studdy Solution

STEP 1

1. The given expression is: $-2^{4} \div 4 - 4 \left( x \div 6 \right) + 10$
2. The expression equals $-2$ , so we set it equal to $-2$ and solve for $x$ .
3. We will follow the order of operations (PEMDAS/BODMAS) while simplifying the expression.

STEP 2

1. Simplify the expression by evaluating exponents and performing division.
2. Rearrange the expression to isolate the term containing $x$ .
3. Solve for $x$ .

STEP 3

Evaluate the exponent in the expression: $-2^{4} = -(2^4) = -16$

STEP 4

Perform the division: $-16 \div 4 = -4$

STEP 5

Substitute the simplified value back into the expression: $-4 - 4 \left( x \div 6 \right) + 10$

STEP 6

Combine the constant terms: $-4 + 10 = 6$

STEP 7

Rewrite the expression: $6 - 4 \left( x \div 6 \right)$

STEP 8

Set the expression equal to $-2$ : $6 - 4 \left( x \div 6 \right) = -2$

STEP 9

Isolate the term containing $x$ by subtracting 6 from both sides: $-4 \left( x \div 6 \right) = -2 - 6$ $-4 \left( x \div 6 \right) = -8$

STEP 10

Simplify the equation by isolating $x$ : $4 \left( x \div 6 \right) = 8$

STEP 11

Divide both sides by 4: $x \div 6 = 2$

STEP 12

Solve for $x$ by multiplying both sides by 6: $x = 2 \times 6$ $x = 12$
Solution: The value of $x$ is $12$ .

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