Q. \(-9 \div 8x – 12 = 68\)

Q: How do I simplify -9\cdot 8x-12=68?

Compute -9\cdot 8=-72. Then -72x-12=68.

Q: How do I solve -72x-12=68 for x?

Add 12: -72x=80. Divide by -72: x=\frac{80}{-72}=-\frac{10}{9}.

Q: What if the problem means -(9\cdot 8x-12)=68?

Interpret as - (72x-12)=68\Rightarrow -72x+12=68\Rightarrow -72x=56\Rightarrow x=-\frac{7}{9}.

Q: Isn’t -9\ 8 x-12=68 ambiguous? How can I check parentheses?

Multiply first if it’s meant as (-9)(8)x-12=68. If parentheses change the sign, x differs. Check the original formatting/source.

Q: How do I verify the answer x=-\frac{10}{9} in the equation -72x-12=68?

Substitute: -72\left(-\frac{10}{9}\right)-12=80-12=68, correct.

Q: What’s the common mistake when solving these one-step linear equations?

Forgetting to distribute the negative sign or dividing by -72 incorrectly. Always move constants first, then divide.

Q: How do I write -\frac{10}{9} in simplest fractional form?

\frac{80}{-72}=-\frac{10}{9} after dividing numerator and denominator by 8.

Answer

We solve \(x-12=-9\cdot 8\). First multiply: \(-9\cdot 8=-72\). Then set \(x-12=-72\).

\[x-12=-72\]

Add 12 to both sides:

\[x=-72+12=-60\]

Final result: \(x=-60\)

Detailed Explanation

We solve the equation:

\[
-9x – 12 = 68
\]

Step 1: Get rid of the constant \(-12\).

The constant \(-12\) is being added to the term \(-9x\). To isolate \(x\), subtract \(12\) from both sides.

\[
-9x – 12 – 12 = 68 – 12
\]

Simplify the right side and the left side:

\[
-9x – 24 = 56
\]

Step 2: Isolate the \(x\) term.

Now \(-9x – 24 = 56\). Next, add \(24\) to both sides to cancel \(-24\) on the left.

\[
-9x – 24 + 24 = 56 + 24
\]

Simplify:

\[
-9x = 80
\]

Step 3: Solve for \(x\).

We have \(-9x = 80\). Divide both sides by \(-9\).

\[
x = \frac{80}{-9}
\]

Simplify the fraction:

\[
x = -\frac{80}{9}
\]

Final Answer:

\[
\boxed{x = -\frac{80}{9}}
\]

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Algebra FAQ

How do I simplify \(-9\cdot 8x-12=68\)?

Compute \(-9\cdot 8=-72\). Then \(-72x-12=68\).

How do I solve \(-72x-12=68\) for \(x\)?

Add 12: \(-72x=80\). Divide by \(-72\): \(x=\frac{80}{-72}=-\frac{10}{9}\).

What if the problem means \(-(9\cdot 8x-12)=68\)?

Interpret as \(- (72x-12)=68\Rightarrow -72x+12=68\Rightarrow -72x=56\Rightarrow x=-\frac{7}{9}\).

Isn’t \(-9\ 8 x-12=68\) ambiguous? How can I check parentheses?

Multiply first if it’s meant as \((-9)(8)x-12=68\). If parentheses change the sign, \(x\) differs. Check the original formatting/source.

How do I verify the answer \(x=-\frac{10}{9}\) in the equation \(-72x-12=68\)?

Substitute: \(-72\left(-\frac{10}{9}\right)-12=80-12=68\), correct.

What’s the common mistake when solving these one-step linear equations?

Forgetting to distribute the negative sign or dividing by \(-72\) incorrectly. Always move constants first, then divide.

How do I write \(-\frac{10}{9}\) in simplest fractional form?

\(\frac{80}{-72}=-\frac{10}{9}\) after dividing numerator and denominator by 8.

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