Is It True Because of Symmetry?

Algebra Level 2

$\large {\color{#69047E}a}{\color{#D61F06}x} + {\color{#20A900}5}{\color{#69047E}b} = {\color{#D61F06}2}{\color{#69047E}a} + {\color{#69047E}b}{\color{#20A900}q} \\\\\\ \large \text{implies} \\\\\\ \large {\color{#D61F06}x} = {\color{#D61F06}2} \text{ and } {\color{#20A900}q}={\color{#20A900}5}.$

True or False?

For all real numbers ${\color{#69047E}a}, {\color{#69047E}b}, {\color{#D61F06}x}, \text{ and } {\color{#20A900}q}$ , the statement above must be true.