Story highlights Moore's case will now go back to the lower court, which will take a second look at his sentencing

He was convicted of the 1980 murder of James McCarble

Washington (CNN) The Supreme Court sided Tuesday with a death row inmate whose lawyers argued that he should not be executed because he is intellectually disabled.

The justices held that a lower court in Texas had used the wrong standard in determining that Bobby James Moore could be put to death. Moore was convicted of the 1980 murder of James McCarble, an employee at the Birdsall Super Market in Houston.

The Supreme Court's opinion sends a strong signal that Texas -- a state that leads the country in executions -- needs to broaden its interpretation of who is ineligible for the death penalty based on intellectual disability.

The justices sent the case back down to the lower court with instructions to apply current medical community understandings of intellectual disability.

Justice Ruth Bader Ginsburg wrote the 5-3 opinion holding that a lower court that ruled against Moore had relied upon outdated standards

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