Question Solve for $\mathbf{x}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ using $\mathbf{x}+6\mathbf{a}-\mathbf{b}=6(\mathbf{x}+\mathbf{a})-(2\mathbf{a}-\mathbf{b})$.

Studdy Solution
Factor out the common factor of $2$ in the numerator.
$$\mathbf{x} = \frac{2(\mathbf{a} - \mathbf{b})}{5}$$
The vector $\mathbf{x}$ in terms of the vectors $\mathbf{a}$ and $\mathbf{b}$ is:
$$\mathbf{x} = \frac{2}{5}(\mathbf{a} - \mathbf{b})$$