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Solve division equations

Division equations represent a multiplicative relationship involving an unknown dividend, typically in forms such as x÷a=bx \div a=b, where aa is nonzero and the quantities are nonnegative rational numbers, including whole numbers, fractions, and decimals. Solving uses multiplication as the inverse of division to preserve equality and determine the unknown, with substitution or multiplication used to verify the result; variable divisors, negative-number equations, and more general rational algebra are beyond this scope.

Detailed Explanation: Solve division equations

To solve a division equation, use multiplication because multiplication is the inverse of division.

Example:

x÷4=7x \div 4=7
  1. The variable xx is being divided by 44.
  2. Multiply both sides by 44 to undo the division:
4(x÷4)=744(x\div 4)=7\cdot 4
  1. Simplify:
x=28x=28
  1. Check the answer by substituting 2828 for xx:
28÷4=728\div 4=7

The statement is true, so the solution is

x=28\boxed{x=28}

Learn by doing: Solve division equations

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Linear Equation - Solve for Box, Two Terms


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