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Lesson 3: Equations with Rational Coefficients (Fractions and Decimals) — Practice Questions

  1. 1. Solve the equation for $x$: $13 = \frac{1}{2}(10x+6)$. $x$ = ___

  2. 2. Solve for $p$: $\frac{1}{3}(p - 2) = \frac{1}{4}(p + 1)$.

    • A. 11
    • B. 5
    • C. 3
    • D. -10
  3. 3. Find the value of $y$ that satisfies the equation: $\frac{1}{4}(y + 3) = \frac{3}{8}$. $y$ = ___

  4. 4. To solve $\frac{1}{6}(z+2) = \frac{2}{3}(z-1)$ by clearing the fractions first, what number should you multiply both sides of the equation by?

    • A. 2
    • B. 3
    • C. 6
    • D. 18
  5. 5. Solve for $n$ in the following equation: $\frac{3}{4}(n - 5) = \frac{3}{2}$. $n$ = ___

  6. 6. To solve the equation $0.04x - 1.3 = 0.18x + 0.5$ by clearing the decimals, what is the smallest whole number you should multiply both sides by?

    • A. 10
    • B. 100
    • C. 1000
    • D. 1
  7. 7. Solve the equation for $w$: $0.9w - 0.4 = 0.6w + 1.1$. The value of $w$ is ___.

  8. 8. Solve for $m$: $0.12m + 0.05 = 0.4m - 1.35$. The value of $m$ is ___.

  9. 9. Which equation is the result of clearing the decimals in $0.07b - 0.3 = 0.2b + 1.25$?

    • A. $7b - 3 = 2b + 125$
    • B. $7b - 30 = 20b + 125$
    • C. $70b - 30 = 20b + 125$
    • D. $7b - 30 = 2b + 125$
  10. 10. Solve for $x$: $0.04x + 0.02 = 0.02x + 0.13$. The value of $x$ is ___.