1. **State the problem:** Simplify the expression $22x + (-3x) + 5x$. 2. **Recall the rule:** When adding or subtracting like terms (terms with the same variable and exponent), you add or subtract their coefficients. 3. **Apply the rule:** Combine the coefficients of $x$: $$22 + (-3) + 5$$ 4. **Simplify step-by-step:** $$22 + (-3) + 5 = 22 - 3 + 5$$ $$= 19 + 5$$ $$= 24$$ 5. **Write the final simplified expression:** $$24x$$ So, $22x + (-3x) + 5x = 24x$.