Q. \(-4.8 = -0.3 x + 3.2\).

Q: How do I solve -4.8 = -0.3x + 3.2 for x?

Move constants: -4.8 - 3.2 = -0.3x . Then -8.0 = -0.3x . Divide: x = \frac{-8.0}{-0.3} \approx 26.67 .

Q: What if I first add 0.3x to both sides and then subtract -4.8 ?

Add 0.3x: 0.3x-4.8=3.2. Subtract 3.2: 0.3x=7.0. Divide: x=\frac{7.0}{0.3}\approx 23.33 (incorrect because the initial rearrangement doesn’t match the original equation signs).

Q: How do I check the solution x \approx 26.67 in the original equation?

Substitute: RHS = -0.3(26.67)+3.2 \approx -8.001+3.2=-4.801, close to -4.8. Small difference is rounding; exact x=\frac{80}{3} gives exact equality.

Q: Can I solve it using the idea “linear equation ax+b=c”?

Rewrite as -0.3x = -4.8 - 3.2 = -8.0 . Then x = \frac{-8.0}{-0.3} . Compute x=\frac{80}{3} \approx 26.67 .

Q: What is the exact value of x without decimals?

Use fractions: -4.8=-\frac{48}{10}=-\frac{24}{5}, -0.3=-\frac{3}{10}, 3.2=\frac{32}{10}=\frac{16}{5}. Then -\frac{24}{5}=-\frac{3}{10}x+\frac{16}{5}. Solve: x=\frac{80}{3}.

Q: Why do negative coefficients require careful sign handling?

When isolating x, dividing by a negative flips signs: from -0.3x=-8.0 , dividing by -0.3 gives x positive. Any sign slip changes the final value.

Answer

We solve the linear equation \( -4.8 = -0.3x + 3.2 \).

Subtract \(3.2\) from both sides:

\[
-4.8 – 3.2 = -0.3x
\]
\[
-8 = -0.3x
\]

Divide both sides by \(-0.3\):

\[
x = \frac{-8}{-0.3} = \frac{8}{0.3} = 26.666\ldots
\]

Final result:

\[
x \approx 26.67
\]

Detailed Explanation

We want to solve the equation:

\[
-4.8 = -0.3x + 3.2
\]

Step 1: Isolate the term with \(x\).

The equation has \(x\) inside the term \(-0.3x\), but there is also a constant \(3.2\) on the right side. We will subtract \(3.2\) from both sides to move it away from the right side.

\[
-4.8 – 3.2 = -0.3x + 3.2 – 3.2
\]

Now simplify both sides.

\[
-8.0 = -0.3x
\]

Step 2: Solve for \(x\).

We have \(-0.3x = -8.0\). To isolate \(x\), divide both sides by \(-0.3\).

\[
x = \frac{-8.0}{-0.3}
\]

Compute the division.

\[
x = \frac{8.0}{0.3}
\]

\[
x = 26.666\ldots
\]

Step 3: Write the final answer.

So the solution is:

\[
x = 26.666\ldots
\]

Equivalently, you can write this as a repeating decimal:

\[
x = 26.\overline{6}
\]

See full solution

Struggling with math? Try our AI homework help tools today.

Homework AI

Algebra FAQ

How do I solve \( -4.8 = -0.3x + 3.2 \) for \(x\)?

Move constants: \( -4.8 - 3.2 = -0.3x \). Then \( -8.0 = -0.3x \). Divide: \( x = \frac{-8.0}{-0.3} \approx 26.67 \).

What if I first add \(0.3x\) to both sides and then subtract \( -4.8 \)?

Add \(0.3x\): \(0.3x-4.8=3.2\). Subtract \(3.2\): \(0.3x=7.0\). Divide: \(x=\frac{7.0}{0.3}\approx 23.33\) (incorrect because the initial rearrangement doesn’t match the original equation signs).

How do I check the solution \(x \approx 26.67\) in the original equation?

Substitute: RHS \(= -0.3(26.67)+3.2 \approx -8.001+3.2=-4.801\), close to \(-4.8\). Small difference is rounding; exact \(x=\frac{80}{3}\) gives exact equality.

Can I solve it using the idea “linear equation \(ax+b=c\)”?

Rewrite as \( -0.3x = -4.8 - 3.2 = -8.0 \). Then \( x = \frac{-8.0}{-0.3} \). Compute \( x=\frac{80}{3} \approx 26.67 \).

What is the exact value of \(x\) without decimals?

Use fractions: \( -4.8=-\frac{48}{10}=-\frac{24}{5}\), \( -0.3=-\frac{3}{10}\), \(3.2=\frac{32}{10}=\frac{16}{5}\). Then \( -\frac{24}{5}=-\frac{3}{10}x+\frac{16}{5}\). Solve: \(x=\frac{80}{3}\).

Why do negative coefficients require careful sign handling?

When isolating \(x\), dividing by a negative flips signs: from \( -0.3x=-8.0 \), dividing by \(-0.3\) gives \(x\) positive. Any sign slip changes the final value.

Use these AI tools to solve!
Check each step for accuracy!

298,376+ active customers
Math, Geometry, Trigonometry, etc.

Math Solver Geometry Solver Trigonometry Solver