Problem 102 - Algebra and Trigonometry

Question

Write each algebraic expression without parentheses. $$\frac{1}{2}(2 y)+[(-7 x)+7 x]$$

Step-by-Step Solution

Answer

The simplified algebraic expression is \[y+0\] which simplifies further to just \[y\].

Step 1: Apply the distribution property

Apply the distribution property, which says a*(b+c)=a*b + a*c, where a is the number outside the parentheses, and b+c is inside the parentheses. Then the algebraic expression becomes: \\[\frac{1}{2}(2y) \\rightarrow \\frac{1}{2}*2*y = y\] and \\[(-7x) + 7x = -7x + 7x\]

Step 2: Simplify the expression

Now simplify each expression. The first simplifies to just y since half of 2 is 1, and the second simplifies to 0 since anything plus its negative counterpart equals zero. \\[\frac{1}{2}(2y) = y\] and \\[(-7x) + 7x = 0\]