Question

name: practice & problem solving for 7-9, write an equivalent expression. 7. -3(7 + 59) 8. (x + 7) + 3y 9. \frac{2}{9} - \frac{1}{5} \cdot x scan for multimedia

Explanation:

Problem 7:

Step1: Apply distributive property

The distributive property states that \(a(b + c)=ab+ac\). Here, \(a = - 3\), \(b = 7\) and \(c = 5g\). So we have \(-3\times7+(-3)\times5g\)

Step2: Calculate each term

\(-3\times7=-21\) and \(-3\times5g = - 15g\)

Step1: Apply associative property of addition

The associative property of addition states that \((a + b)+c=a+(b + c)\). Here, \(a=x\), \(b = 7\) and \(c = 3y\). So we can rewrite \((x + 7)+3y\) as \(x+(7 + 3y)\) (or also \(x+3y + 7\) by commutative property)

Step1: Recall order of operations (multiplication before subtraction)

We first perform the multiplication \(\frac{1}{5}\cdot x=\frac{x}{5}\)

Step2: Rewrite the expression

The expression \(\frac{2}{9}-\frac{1}{5}\cdot x\) can be written as \(\frac{2}{9}-\frac{x}{5}\) (we can also get a common denominator, but the problem just asks for an equivalent expression, so this is sufficient)

Answer:

\(-21 - 15g\)

Problem 8: