1. Problem: Solve the multi-step equations given. 2. Formula and rules: To solve linear equations, combine like terms, isolate the variable term, then divide both sides by the coefficient of the variable. 3. Solve each: a) $5 + 3x + 4x = 19$ Combine like terms: $5 + 7x = 19$ Subtract 5: $\cancel{5} + 7x = 19 - \cancel{5}$ $7x = 14$ Divide by 7: $\frac{7x}{\cancel{7}} = \frac{14}{\cancel{7}}$ $x = 2$ b) $15y - 6 - 10y = 9$ Combine like terms: $5y - 6 = 9$ Add 6: $5y - \cancel{6} + \cancel{6} = 9 + 6$ $5y = 15$ Divide by 5: $\frac{5y}{\cancel{5}} = \frac{15}{\cancel{5}}$ $y = 3$ c) $32 = 5 - 4a - 5a$ Combine like terms: $32 = 5 - 9a$ Subtract 5: $32 - \cancel{5} = \cancel{5} - 9a - \cancel{5}$ $27 = -9a$ Divide by -9: $\frac{27}{\cancel{-9}} = \frac{-9a}{\cancel{-9}}$ $-3 = a$ d) $5m + 3 - 9m + 13 = 0$ Combine like terms: $-4m + 16 = 0$ Subtract 16: $-4m + \cancel{16} - \cancel{16} = 0 - 16$ $-4m = -16$ Divide by -4: $\frac{-4m}{\cancel{-4}} = \frac{-16}{\cancel{-4}}$ $m = 4$ e) $6w + 8 = 4w + 18$ Subtract $4w$: $6w - 4w + 8 = 4w - 4w + 18$ $2w + 8 = 18$ Subtract 8: $2w + \cancel{8} - \cancel{8} = 18 - 8$ $2w = 10$ Divide by 2: $\frac{2w}{\cancel{2}} = \frac{10}{\cancel{2}}$ $w = 5$ f) $-8x - 5 = 2x + 15$ Add $8x$: $-8x + 8x - 5 = 2x + 8x + 15$ $-5 = 10x + 15$ Subtract 15: $-5 - 15 = 10x + 15 - 15$ $-20 = 10x$ Divide by 10: $\frac{-20}{\cancel{10}} = \frac{10x}{\cancel{10}}$ $-2 = x$ Final answers: a) $x=2$ b) $y=3$ c) $a=-3$ d) $m=4$ e) $w=5$ f) $x=-2$