Question

LOGICAL REASONING Decide whether the statement is true or false If false, rewrite the right-hand side of the equation so the statement is true. $$ 3(2+7) \stackrel{?}{=} 3(2)+7 $$

Short answer

The statement \(3(2+7) = 3(2)+3*7\) is true. No modification is needed for the right-hand side of the equation.

Step-by-step solution

Understand the problem

The equation presented is \(3(2+7) \stackrel{?}{=} 3(2)+7\). The objective is to evaluate whether the equation is true or false. If it is false, then modify the right side of the equation to make the statement true.

Apply Distributive Property

First, simplify the expression on the left side of the equation by executing the operation inside the parentheses and multiplying by 3. This gives \(3 * 9 = 27\). Then for the right side of the equation, distribute the 3 to both terms inside the parentheses, giving \(3*2 + 3*7 = 6 + 21 = 27\). Thus the equation reads \(27 = 27\).

Compare Both Sides

Finally, compare the simplified results on both sides of the equation. We have 27 on both sides which shows that the initial equation holds true. Therefore, there is no need to rewrite the right-hand side of the equation.