Q. \(3.8 – 2.5x = 4.16\)

Q: How do I isolate x in 3.8-2.5x=4.16?

Add 2.5x to both sides: 3.8=4.16+2.5x. Then subtract 4.16: 3.8-4.16=2.5x. So x=\dfrac{3.8-4.16}{2.5}.

Q: Should x be negative here?

Yes. Since 3.8 is less than 4.16, the term -2.5x must be negative to raise the left side, so x is negative.

Q: How can I check the solution x=-0.144?

Compute 3.8-2.5(-0.144)=3.8+0.36=4.16, which matches the right side.

Answer

We solve the equation \(3.8 – 2.5x = 4.16\).

\(3.8 – 2.5x = 4.16 \Rightarrow -2.5x = 4.16 – 3.8 = 0.36\).

\(-2.5x = 0.36 \Rightarrow x = \dfrac{0.36}{-2.5} = -0.144\).

Final result: \(x = -0.144\).

Detailed Explanation

Problem: Solve the equation

\[
3.8 – 2.5x = 4.16
\]

Step 1: Get the variable term by itself.

Right now, the variable term is \(-2.5x\), but there is also \(3.8\) on the left. To undo the \(3.8\), subtract \(3.8\) from both sides.

\[
3.8 – 2.5x – 3.8 = 4.16 – 3.8
\]

Now simplify both sides.

\[
-2.5x = 0.36
\]

Step 2: Solve for \(x\).

We have \(-2.5x = 0.36\). To isolate \(x\), divide both sides by \(-2.5\).

\[
x = \frac{0.36}{-2.5}
\]

Step 3: Compute the division.

\[
x = -0.144
\]

Final Answer:

\[
\boxed{x = -0.144}
\]

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Algebra FAQ

How do I isolate \(x\) in \(3.8-2.5x=4.16\)?

Add \(2.5x\) to both sides: \(3.8=4.16+2.5x\). Then subtract \(4.16\): \(3.8-4.16=2.5x\). So \(x=\dfrac{3.8-4.16}{2.5}\).

What is \(3.8-4.16\)?

\(3.8-4.16=-0.36\).

What is \(x\) after dividing by \(2.5\)?

\(x=\dfrac{-0.36}{2.5}=-0.144\).

Should \(x\) be negative here?

Yes. Since \(3.8\) is less than \(4.16\), the term \(-2.5x\) must be negative to raise the left side, so \(x\) is negative.

How can I check the solution \(x=-0.144\)?

Compute \(3.8-2.5(-0.144)=3.8+0.36=4.16\), which matches the right side.

Solve 3.8−2.5x=4.16 fast.
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