Question

convince me! what property can you use to write an equivalent expression for -5(x - 2)? explain.

Explanation:

Step1: Recall the Distributive Property

The distributive property states that for any real numbers \(a\), \(b\), and \(c\), \(a(b - c)=ab - ac\) (or more generally \(a(b + c)=ab+ac\)). Here, we have \(-5(x - 2)\), where \(a=-5\), \(b = x\), and \(c = 2\).

Step2: Apply the Distributive Property

Using the distributive property \(a(b - c)=ab - ac\), substitute \(a=-5\), \(b = x\), and \(c = 2\) into the formula. So we get \(-5\times x-(-5)\times2\).

Step3: Simplify the Expression

Simplify \(-5\times x\) to \(-5x\) and \(-(-5)\times2\) to \(10\) (because multiplying two negative numbers gives a positive number, \(-5\times(- 2)=10\)). So the equivalent expression is \(-5x + 10\).

Answer:

We can use the distributive property (also known as the distributive property of multiplication over subtraction). The distributive property states that \(a(b - c)=ab - ac\) for real numbers \(a\), \(b\), and \(c\). For \(-5(x - 2)\), applying the distributive property: let \(a=-5\), \(b = x\), and \(c = 2\). Then \(-5(x - 2)=-5\times x-(-5)\times2=-5x + 10\). So the distributive property is used to write the equivalent expression \(-5x + 10\) for \(-5(x - 2)\).