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In equations, isolating the variable is the first step in solving for unknowns. The idea is to have the variable alone on one side of the equation, usually the left side. In our equation, \(-\frac{7}{16}h + 28 = 21\), this means moving any constants (numbers without the variable) to the other side.

We start by eliminating the constant 28 from the left side by subtracting 28 from both sides. When we do this, \(-\frac{7}{16}h + 28 - 28 = 21 - 28\), which simplifies to\(-\frac{7}{16}h = -7\). The key here is to perform the same operation (subtracting 28) to both sides of the equation. This keeps the equation balanced, which is crucial for maintaining equality.

After you find a solution for the variable, it's important to verify that it's correct. This process of checking ensures that your solution truly satisfies the original equation.

To check the solution, substitute the value of the variable back into the original equation to see if the equation holds true. Here's how we do it:

• Substitute \(h = 16\) back into the equation \(-\frac{7}{16}(16) + 28 = 21\).
• Calculate the product \(-\frac{7}{16} \times 16\), yielding \(-7\).
• Evaluate the expression \(-7 + 28\) and check if it equals 21.
• We find that it does equal 21, confirming the solution is correct.

Checking your work is an essential step that ensures you didn’t make errors during the earlier steps. It builds confidence that you've solved the equation accurately.

When dealing with coefficients in fractions, reciprocal multiplication is a handy tool. If you have a fraction as a coefficient, like \(-\frac{7}{16}\) in our equation, you can use its reciprocal to solve for the variable.

A reciprocal is simply flipping the fraction. For \(-\frac{7}{16}\), the reciprocal is \(-\frac{16}{7}\). Multiplying both sides of the equation by this reciprocal will effectively "cancel out" the fraction, allowing you to isolate the variable.

Here's how it works with our equation: \[-\frac{7}{16}h = -7\]. Multiplying both sides by \(-\frac{16}{7}\), we get

• \(h = -7 \times -\frac{16}{7}\)
• Multiply and simplify: \(h = 16\)

The multiplication of a number by its reciprocal results in 1, effectively removing the fraction and making it easier to solve for the variable. Reciprocal multiplication is a powerful method to tackle fractional coefficients efficiently.