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Quiz 4
1. Calculate $2^2[(1+3^2 \cdot 2)+1]$.
Solution: Calculate using the order of operations: $$\begin{array}{ll} 2^2[(1+3^2 \cdot 2)+1] &= 2^2 [ (1+9 \cdot 2)+1 ] \\ &= 2^2 [ (1+18)+1] \\ &= 2^2 [ 19 + 1 ] \\ &= 2^2 [ 20 ] \\ &= 4 \cdot 20 \\ &= 80. \end{array}$$

2. Calculate $2 \cdot 3 + [1-(2 \cdot 2 + 4)]^2$.
Solution: Calculate using the order of operations: $$\begin{array}{ll} 2 \cdot 3 + [1-(2 \cdot 2+ 4)]^2 &= 2 \cdot 3 + [1- (4+4)]^2 \\ &=2 \cdot 3 + [1 - 8]^2 \\ &= 2 \cdot 3 + [-7]^2 \\ &= 2 \cdot 3 + 49 \\ &= 6 + 49 \\ &= 55. \end{array}$$

3. Is $3$ a solution of $2x+1=9$?
Solution: No. Because when substituting $x=3$ into the equation, we get the equation $$2\cdot 3 + 1 = 9,$$ which is a false equation.

4. Solve $x-5=13$.
Solution: We add $5$ to both sides using the "addition principle" to get $$x-5+5 = 13+5.$$ Now simplify and we get $$x+0=18,$$ or $$x=18.$$

5. Solve $2x-5=x+2$.
Solution: Add $5$ to both sides to get $$2x = x+7.$$ Add $-x$ to both sides to get $$x = 7.$$