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Chapter 6: Problem 91

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \((3 y-4)-(8 y-1)=-5 y-3\)

Short Answer

Expert verified
The statement \((3 y-4)-(8 y-1)=-5 y-3\) is true.

Step by step solution

01

Expand the brackets

Start with the equation \((3y - 4) - (8y - 1)\). The first part is \(3y - 4\) and on subtracting the second part, which is \(8y - 1\), you get \(3y - 4 - 8y + 1\). Note that the signs within the brackets get inverted when the brackets are removed.
02

Simplify the equation

Now, combine like terms: \(3y - 8y\) gives \(-5y\) and \(-4 + 1\) gives \(-3\). This simplifies the equation to \(-5y - 3\).
03

Check for equality to validate the statement

Finally, to determine the truth of the statement, compare \(-5y - 3\) to the expression on the right hand side of the equation given, which is \(-5y - 3\). As you can see, both the expressions are the same, therefore, the statement is true.

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Use FOIL to find the products. \((3 x-7)(4 x-5)\)

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