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x = 6.
4x + 10 + 3x = 52
We can add the x's together (combine the terms) to get:
7x + 10 = 52 (the plus 4x and the plus 3x become plus 7x here).
Now we can combine the constants (the numbers) by moving the plus 10 to the same side of the equation as the plus 52. When we move something from one side of an equation to the other we must swap the sign (a plus becomes a negative and a negative becomes a plus). So we get:
7x = 52 - 10 (in effect we have actually subtracted 10 from BOTH sides of the equation to keep the equation balanced).
Now we simplify:
7x = 42
x = 42/7
x = 6.
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