Question

solve using the multiplication principle. dont forget to perform a check.
$-\frac{5}{6}x = -\frac{9}{10}$

Explanation:

Step1: Isolate x via reciprocal multiply

Multiply both sides by $\frac{6}{-5}$:
$$-\frac{5}{6}x \times \frac{6}{-5} = -\frac{9}{10} \times \frac{6}{-5}$$

Step2: Simplify right-hand side

Cancel common factors and compute:
$$x = \frac{9 \times 6}{10 \times 5} = \frac{54}{50} = \frac{27}{25}$$

Step3: Verify solution

Substitute $x=\frac{27}{25}$ into original equation:
$$-\frac{5}{6} \times \frac{27}{25} = -\frac{135}{150} = -\frac{9}{10}$$
This matches the right-hand side.

Answer:

$x=\frac{27}{25}$