# Question Video: Solving Linear Equations with an Unknown Mathematics • 6th Grade

Given that 5 + 𝑛 = −5, find the value of 𝑛.

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### Video Transcript

Given that five plus 𝑛 equals negative five, find the value of 𝑛.

We have the equation five plus 𝑛 equals negative five. This is telling us that when we add some value to five, the result is negative five. To find out what 𝑛 is, we need to think about the inverse property of addition. The inverse property of addition says that any number added to its opposite will equal zero. Since five and 𝑛 are being added together, if we subtract five, then five minus five will equal zero. But we also know the subtraction property of equality, which tells us that if we subtract five from one side of the equation, we must subtract five from the other side of the equation to keep it balanced. If five minus five is zero, then on the left side of the equal sign, we only have the variable 𝑛. And on the right side, we have negative five minus five, which equals negative 10. And so, we found that 𝑛 equals negative 10.

If you start with five and add negative 10 to that five, you’ll get negative five. This is a vertical method for solving the problem. We do this by writing the next line directly under the line above it. The other way to do it would be to use a horizontal method. We began with five plus 𝑛 equals negative five. But then, in the next line, we’ll add the negative five in the row with our original equation. So that it says five minus five plus 𝑛 equals negative five minus five. Both methods show that 𝑛 is equal to negative 10.