1. **Stating the problem:** Solve the linear equations with multiple terms for $x$. 2. **Formula and rules:** To solve equations like these, combine like terms (all $x$ terms together and constants together) on each side, then isolate $x$ by moving terms and dividing. 3. **Example given:** $$26x - 12 - 46x - 21 = 8 - 22x + 23 - 14x$$ Combine like terms: $$26x - 46x + 22x + 14x - 12 - 21 = 8 + 23$$ Simplify: $$16x - 33 = 31$$ Add 33 to both sides: $$16x = 64$$ Divide both sides by 16: $$x = 4$$ 4. **Solve each exercise:** **a)** $13x + 14 - 17x + 12 = 106 - 8x$ Combine like terms: $$13x - 17x + 8x = 106 - 14 - 12$$ $$4x = 80$$ Divide by 4: $$x = 20$$ **b)** $3x + 11 = x + 16$ Move $x$ terms: $$3x - x = 16 - 11$$ $$2x = 5$$ Divide by 2: $$x = 2.5$$ (Note: user wrote $x=13.5$ but correct is $2.5$) **c)** $17x - 117 = 5x - 9$ Move $x$ terms and constants: $$17x - 5x = -9 + 117$$ $$12x = 108$$ Divide by 12: $$x = 9$$ **d)** $54x - 7 = 85 - 66x + 78$ Combine constants on right: $$54x - 7 = 163 - 66x$$ Move $x$ terms: $$54x + 66x = 163 + 7$$ $$120x = 170$$ Divide by 120: $$x = \frac{170}{120} = \frac{17}{12} \approx 1.4167$$ **e)** $289 + 196x = 169x + 343$ Move $x$ terms and constants: $$196x - 169x = 343 - 289$$ $$27x = 54$$ Divide by 27: $$x = 2$$ **f)** $45 + 14x + 1 = 11x + 47 + 2x$ Simplify left and right: $$46 + 14x = 13x + 47$$ Move $x$ terms and constants: $$14x - 13x = 47 - 46$$ $$x = 1$$ **g)** $16.81x - 7.83 - 7.35x = 8.65x - 7.29$ Combine $x$ terms left: $$9.46x - 7.83 = 8.65x - 7.29$$ Move $x$ terms and constants: $$9.46x - 8.65x = -7.29 + 7.83$$ $$0.81x = 0.54$$ Divide by 0.81: $$x = \frac{0.54}{0.81} = \frac{2}{3} \approx 0.6667$$ **h)** $46 - 42x = 36 - 45x + 10$ Combine constants right: $$46 - 42x = 46 - 45x$$ Move $x$ terms: $$-42x + 45x = 46 - 46$$ $$3x = 0$$ $$x = 0$$ 5. **Summary:** Each equation is solved by combining like terms, moving all $x$ terms to one side and constants to the other, then dividing to isolate $x$. Final answers: a) $x=20$ b) $x=2.5$ c) $x=9$ d) $x=\frac{17}{12}$ e) $x=2$ f) $x=1$ g) $x=\frac{2}{3}$ h) $x=0$