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At first, the question "What is righteousness?" may seem like a "no-brainer" because we know it means "rectitude," or more simply, "right doing." By quoting Psalm 119:172, "All Your commandments are righteousness," we feel equipped with a direct biblical definition of this important biblical concept. None of these is wrong, but the Bible's use of "righteousness" is both specific and broad—so broad that in some places it is treated as a synonym of salvation itself (Isaiah 45:8; 46:12-13; 51:5; 56:1; 61:10).
Though the Bible uses "righteousness" so broadly, its comparison with "salvation" does not help us much in understanding it because "salvation" is one of the Bible's most comprehensive terms. Since none of us has fully experienced salvation, we look through a glass darkly trying to comprehend it.
Righteousness is used in a similar sense in the very familiar passage given in Matthew 6:33, where Jesus commanded, "But seek first the kingdom of God and His righteousness, and all these things shall be added to you." Here it has the sense of seeking all of God's spiritual blessings, favor, image, and rewards. We see in this verse not only a broad New Testament application of the term but also, more importantly, its priority to life. This dovetails perfectly with the hunger-and-thirst metaphor. It is not enough to ambitiously yearn to accomplish. According to Jesus, God's Kingdom and His righteousness are the very top priorities in all of life. Seeking God's righteousness is that important.
John W. Ritenbaugh
The Beatitudes, Part Four: Hungering and Thirsting After Righteousness