Solving an equation means finding all values that make it true. Equality is preserved by adding or subtracting the same quantity on both sides, or multiplying or dividing both sides by the same nonzero number. Expand brackets and clear numerical denominators before collecting terms. Example 2x-13+2=5 2x-1+6=15 2x=10 x=5. Check: 2(5)-13+2=5. Substitution checks the original equation, not just the final line. An equation may simplify to a true statement such as 0=0, giving every permitted value, or a false statement such as 0=4, giving no solution.

Solving an equation means finding all values that make it true. Equality is preserved by adding or subtracting the same quantity on both sides, or multiplying or dividing both sides by the same nonzero number. Expand brackets and clear numerical denominators before collecting terms.

\(\begin{aligned}\dfrac{2x-1}{3}+2&=5\\2x-1+6&=15\\2x&=10\\x&=5.\end{aligned}\)

Check: \(\dfrac{2(5)-1}{3}+2=5\). Substitution checks the original equation, not just the final line.

An equation may simplify to a true statement such as \(0=0\), giving every permitted value, or a false statement such as \(0=4\), giving no solution.

Equivalent equations

Equivalent equations