Solve the linear equation −0.00143x + 0.06997 = 0.297 for x.

Step-by-step solution

1. 1

   Isolate the x term. Subtract the constant from both sides, lining the decimals up carefully:

   $-0.00143x = 0.297 - 0.06997 = 0.22703$

   Writing $0.297$ as $0.29700$ before subtracting is what prevents the classic place-value slip here.

2. 2

   Divide by the coefficient, keeping track of the sign. The coefficient is negative, so the quotient of a positive by a negative is negative:

   $x = \frac{0.22703}{-0.00143}$

   A sign check up front is worth doing: the line $y = -0.00143x + 0.06997$ decreases, and the target $0.297$ is above the intercept $0.06997$, so $x$ must be negative.

3. 3

   Clear the decimals to get an exact value. Multiply numerator and denominator by $100{,}000$:

   $x = \frac{22703}{-143} = -\frac{22703}{143}$

   Since $143 = 11 \times 13$ and $22703 = 143 \times 158 + 109$, the fraction does not reduce, so this is the exact answer.

4. 4

   Convert to a decimal. Long division gives

   $x = -158.\overline{762237} \approx -158.7622$

   Rounded to four decimal places, $x \approx -158.7622$.

5. 5

   Substitute back to verify. Using the exact value,

   $-\frac{143}{100000}\left(-\frac{22703}{143}\right) + \frac{6997}{100000} = \frac{22703 + 6997}{100000} = \frac{29700}{100000} = 0.297 \ \checkmark$

   The exact arithmetic closes with no rounding at all, confirming both the sign and the magnitude.