Question

When solving equations it is important to think about how the equation is built. Theidea is to figure out what operations were done to x, then undo these in the oppositeorder. Solve these, using a calculator only when necessary. Assums x is positiveExample: 5x' = 40Solution: x is first raised to the power, then multiplied by 5. We can undo theexpression by first dividing both sides by 5, then raising both sides to the powerx=8. (x+)' -8= 16. Therefore * = 16a) 2X ¼= 6?b) (2X) ¼= 6?c) x-² +3= 8?

Answer 1

a)

$\frac{2x}{4}=6$

Solution: we can multiply x by 2 and divide by 4, so to solve for x, we can multiply bout sides of the eqution by 4/2 so:

$\begin{gathered} \frac{4}{2}\frac{2x}{4}=\frac{4}{2}6 \\ x=\frac{24}{2}=12 \\ x=12 \end{gathered}$

b)

$(2x)\frac{1}{4}=6$

first we can multiply by 4 so:

$\begin{gathered} (2x)\frac{4}{4}=6\cdot4 \\ 2x=24 \end{gathered}$

and now we can divide by 2 so:

$\begin{gathered} \frac{2x}{2}=\frac{24}{2} \\ x=12 \end{gathered}$

c)

$x^2+3=8$

so we can rest 3 un bout sides of the equation:

$\begin{gathered} x^2+3-3=8-3 \\ x^2=5 \end{gathered}$

Now we can use the square root to solve for x so:

$\begin{gathered} \sqrt[]{x^2}=\sqrt[]{5} \\ x=\sqrt[]{5} \end{gathered}$