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Some equations have variables on each side of the equals sign, for example \(4 (k + 7) = 12k - 4\).

Solve \(4(k + 7) = 12k - 4\).

\(4k + 28 = 12k - 4\)

Decide which of the unknowns has the smaller number in front of it. 4 is less than 12 so subtract \(4k\) from both sides.

\(\begin{array}{ccc} 4k + 28 & = & 12k - 4 \\ -4k && -4k \end{array}\)

\(28 = 8k - 4\)

Isolate the term \(8k\) on the right hand side by adding 4 to each side:

\(\begin{array}{ccc} 28 & = & 8k - 4 \\ +4 && +4 \end{array}\)

\(32 = 8k\)

Isolate \(k\) by dividing both sides by 8:

\(\begin{array}{ccc} 32 & = & 8k \\ \div 8 && \div 8 \end{array}\)

\(4 = k\)

Substituting \(k = 4\) back into the original equation gives:

Left hand side: \(4k + 28 = 4 \times 4 + 28 = 16 + 28 = 44\)

Right hand side: \(12k - 4 = 12 \times 4 - 4 = 48 -4 = 44\)

The equation balances, so \(k = 4\) is the correct solution.