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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
$$x = 7.$$
