Worksheet: Solving Literal Equations

**Instructions:** Solve each equation for the indicated variable.

**1.** Solve for \(x\): \(2y + 3x = 10\)

**2.** Solve for \(y\): \(4x – 3y = 12\)

**3.** Solve for \(a\): \(2b – 3a = 5\)

**4.** Solve for \(b\): \(3a + 2b = 8\)

**5.** Solve for \(h\): \(A = \frac{1}{2}bh\)

**6.** Solve for \(r\): \(V = \frac{4}{3}\pi r^3\)

**7.** Solve for \(t\): \(d = rt\)

**8.** Solve for \(p\): \(A = p(1 + rt)\)

**9.** Solve for \(c\): \(F = \frac{9}{5}C + 32\)

**10.** Solve for \(C\): \(K = C + 273.15\)

**Remember:** To solve a literal equation, isolate the indicated variable on one side of the equation using inverse operations. Treat letters as variables just like numbers.

**Answers:**
1. \(x = \frac{10 – 2y}{3}\)
2. \(y = \frac{4x – 12}{3}\)
3. \(a = \frac{2b – 5}{3}\)
4. \(b = \frac{8 – 3a}{2}\)
5. \(h = \frac{2A}{b}\)
6. \(r = \sqrt[3]{\frac{3V}{4\pi}}\)
7. \(t = \frac{d}{r}\)
8. \(p = \frac{A}{1 + rt}\)
9. \(c = \frac{5}{9}(F – 32)\)
10. \(C = K – 273.15\)

Ensure that you perform the operations correctly when isolating the variable. Double-check your solutions by substituting them back into the original equations!

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