Subjects algebra

Solve Arrange Equations C07D65

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1. **State the problem:** Solve each equation for the variable and then arrange the solutions in numerical order from least to greatest. 2. **Equation 1:** $-5n - 8(1 + 7n) = -8$ Use the distributive property: $$-5n - 8 - 56n = -8$$ Combine like terms: $$-5n - 56n - 8 = -8$$ $$-61n - 8 = -8$$ Add 8 to both sides: $$-61n - 8 + 8 = -8 + 8$$ $$-61n = 0$$ Divide both sides by $-61$: $$\cancel{-61}n = \frac{0}{\cancel{-61}}$$ $$n = 0$$ 3. **Equation 2:** $37 = -3 + 5(x + 6)$ Distribute 5: $$37 = -3 + 5x + 30$$ Combine constants on the right: $$37 = 5x + 27$$ Subtract 27 from both sides: $$37 - 27 = 5x + 27 - 27$$ $$10 = 5x$$ Divide both sides by 5: $$\frac{10}{\cancel{5}} = \frac{5x}{\cancel{5}}$$ $$2 = x$$ 4. **Equation 3:** $-13 = 5(1 + 4m) - 2m$ Distribute 5: $$-13 = 5 + 20m - 2m$$ Combine like terms: $$-13 = 5 + 18m$$ Subtract 5 from both sides: $$-13 - 5 = 5 + 18m - 5$$ $$-18 = 18m$$ Divide both sides by 18: $$\frac{-18}{\cancel{18}} = \frac{18m}{\cancel{18}}$$ $$-1 = m$$ 5. **Arrange solutions in numerical order:** $$m = -1, n = 0, x = 2$$ **Final answer:** The solutions in order from least to greatest are $-1, 0, 2$.