1Cademy - Solving $$rac{2s+3}{2} + 1 = rac{3s+2}{4}$$ by Clearing Fractions

Learn Before

Strategy for Solving Equations with Fraction or Decimal Coefficients

Example

Solving $rac{2s+3}{2} + 1 = rac{3s+2}{4}$ by Clearing Fractions

To solve the linear equation $rac{2s+3}{2} + 1 = rac{3s+2}{4}$ by clearing fractions, first find the LCD for the denominators $2$ and $4$ , which is $4$ . Multiply every term on both sides by $4$ , ensuring the integer term $1$ is also multiplied by the LCD:

ight) + 4(1) = 4\left( rac{3s+2}{4} ight)$$ Simplify the terms to remove the fractions: $$2(2s+3) + 4 = 3s+2$$ Distribute the $$2$$ on the left side: $$4s+6+4=3s+2$$ Combine the constant terms on the left: $$4s+10=3s+2$$ Collect the variable terms to the left by subtracting $$3s$$ from both sides: $$s+10=2$$ Subtract $$10$$ from both sides to isolate the variable: $$s=-8$$ Checking the solution by substituting $$-8$$ in the original equation confirms the solution.

Updated 2026-04-22

Contributors are:

Who are from:

References

OpenStax Intermediate Algebra

Learn Before

Related